Search is not available for this dataset
uuid string | license string | generator string | version string | category string | reasoning string | messages list |
|---|---|---|---|---|---|---|
9c691c36-b28b-4a8d-a697-17fe2e6cd9de | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSolve the equation $\\sin 2x = \\cos 3x$."
},
{
"role": "assistant",
"content": "<think></think>\nThe equation to so... |
5dce04f0-faa9-4fe6-ab60-fb5ee5ce2fd1 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nCalculate the indefinite integral $\\int (ax^2+bx+c)e^{mx} \\, dx$ where $abcm \\neq 0$."
},
{
"role": "assistant",
... |
55c72f18-4660-4bf9-95cd-5b9022794853 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the pentagon $ABCDE$ inscribed in a given circle such that $AC \\perp BE$ and the area is maximized."
},
{
"role": ... |
3e8d4c0e-0499-494b-8af9-d4e1b72f7cfa | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFor what minimum $n$ can one mark $n$ points on a circle so that among the triangles with vertices at the marked points there ar... |
6249681b-c253-4aa7-a09d-2694e4f69489 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all functions \\( f: \\mathbb{Z} \\to \\mathbb{Z} \\) such that for any integers \\( a \\), \\( b \\), and \\( c \\) satisf... |
27f09f98-9dd5-4f74-8eda-44011ef69a0b | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nEvaluate the sum \\( \\frac{100}{2 \\cdot 1} + \\frac{100}{2 \\cdot 3} + \\frac{100}{3 \\cdot 4} + \\cdots + \\frac{100}{99 \\cd... |
35dc1c51-2f89-4686-958f-f5a8d0ae87fe | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all functions \\( f \\) satisfying \\( f(y + f(x)) = f(x)f(y) + f(f(x)) + f(y) - xy \\) for all real numbers \\( x \\) and ... |
47e24e1a-8051-48f3-8d4f-78aad5900969 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the total number of integral solutions to the equation $x^2 + y^2 + z^2 + t^2 = 2^{2004}$, where $0 \\leq x \\leq y \\leq z... |
33e799ae-27b0-4552-bf0b-65547aa8bab8 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSolve the following equations applying the methods presented above. $2\\tan x+\\tan 2x=\\tan 4x$."
},
{
"role": "assista... |
70ddb95d-3030-495e-93c7-d2682a99271f | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nAn increasing sequence \\(a_{1}, a_{2}, \\dots, a_{k}\\) of positive integers satisfies \\(a_{1} = 2024\\) and the condition \\(... |
c206aa67-3f1b-44bb-a2c3-a7c0dfd1c713 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nConsider a monotonic increasing function \\( f : [1,\\infty) \\rightarrow (1,\\infty) \\) such that for any real number \\( x \\... |
4c8759ba-f986-46b2-8325-6d41499a3f5a | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nEvaluate the limit \\(\\lim_{x \\to -1^+} \\frac{\\sqrt{\\pi} - \\arccos(x)}{\\sqrt{x+1}}\\)."
},
{
"role": "assistant",... |
9b4a40fb-b0bd-4650-bdc6-a0e4b097de17 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nCompute the Galois group of the extension of $\\mathbb{Q}$ to the splitting field of the polynomial $f = x^5 - 5$."
},
{
... |
9807dd98-8425-46a9-ae51-3f3518071557 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\( U \\) be the set of all one-to-one functions \\( f: \\{1, 2, \\ldots, 10\\} \\rightarrow \\{1, 2, \\ldots, 10\\} \\). Le... |
6db12485-d1ba-4011-b3f1-b178a1d4679e | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDefine \\( S(x) = \\left( \\frac{\\sin{\\pi x}}{\\pi x} \\right)^2 \\), which has the Fourier transform \\( \\hat{S}(\\xi) = 1 -... |
57ef5540-6bfd-403d-8629-9ccbed2519fe | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn triangle \\(ABC\\), \\(\\angle ABC = 138^\\circ\\) and \\(\\angle ACB = 24^\\circ\\). Point \\(D\\) is on \\(AC\\) such that ... |
3b1b7fce-53ae-43e3-a2cc-60dac5223954 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all continuous positive functions \\( f(x) \\) for \\( 0 \\le x \\le 1 \\) such that\n\\[\n\\int_0^1 f(x) \\, dx = 1, \\qua... |
a491aa70-1a8f-4578-80b4-537a8597ced6 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIf \\( a > 3b > 0 \\), find the maximum value of \\(\\frac{3a + 8a^2b - 16ab^2}{8b^2 - 4ab}\\)."
},
{
"role": "assistant... |
967a450b-2460-4d5f-ac75-0fe5b623ae80 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the number of three-letter code words between DXY and YAZ, excluding these two words, where the letters used are A, B, C, D... |
b0c7dc2a-e469-4393-96af-ccadc0d80cc9 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind an explicit formula for the polynomial recurrence \\( P_{n+1}(x) = x P_n(x) + x^2 P_n'(x) \\) when \\( P_1(x) = 1 \\)."
}... |
12f96e6b-234d-4188-b244-2e04085c021a | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all integers \\( n \\geq 3 \\) such that for any two natural numbers \\( m, r < n-1 \\), there exist \\( m \\) distinct ele... |
8b36235e-3bae-4464-8635-256d2a1e8920 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nThe value of \\(a + b + c + d\\) that satisfies the equations \\(ab + cd = 34\\) and \\(ac - bd = 19\\) is?"
},
{
"role"... |
c1269d94-69ca-403f-b393-925aad402c8c | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nTwo points $A$ and $B$ lie on a regular hexagon, such that $\\overline{AB}$ divides the hexagon into two pentagons. Both pentago... |
778fd709-ae44-4f51-95af-25dec02e79d2 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA bag contains 3 black, 4 white, and 2 red balls, all of which are different. How many ways can at most 6 balls be selected such... |
cb8a52a7-94d7-4eb2-877c-290ca3b1a37b | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the equation of the normal line to the conic \\(x^2 = 4y\\) that passes through the point \\((1, 2)\\)."
},
{
"role... |
68272d25-32e6-4ea5-a73a-0acc776efbc1 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the number of integer ordered pairs $(a, b)$ that satisfy the equation $4^a + 4a^2 + 4 = b^2$."
},
{
"role": "assis... |
67868b6d-dc1d-40f4-9a9d-e44e729ed3cf | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nEvaluate the sum \\(\\sum_{k=0}^{\\lfloor n/2 \\rfloor} C(n-2k, k) \\left(-\\frac{4}{27}\\right)^k\\)."
},
{
"role": "as... |
8a5f15d8-5ad7-479e-9461-66c920125306 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\(\\alpha, \\beta, \\gamma\\) be the roots of the polynomial \\(x^3 + 8x + 1 = 0\\). Find the value of \n\\[\n\\frac{\\beta... |
c17ce345-20e2-4ca7-aed3-843229569f85 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the limit of the sequence \\( a_n = \\frac{(n + 1)^{n + 1} - n^n}{n^{n + 1} - (n + 1)^n} \\)."
},
{
"role": "assist... |
8df24c74-15a8-4096-9da0-0b4452711baf | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSolve the system of equations\n\\[ mx + y + Nz = m + 1 \\]\n\\[ Nx - y + z = N - 1 \\]\n\\[ x - Ny + 5z = 1 - N \\]\nusing Crame... |
a9c23545-01f3-4bb7-bc2a-6797e6265a5d | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDetermine the minimum possible value of positive integer \\( b \\) such that for every integer \\( a \\),\n\\[ \\min{\\left( a^2... |
960c6df7-46d9-46b5-ba1e-9a092b0e4586 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the range of the real constant $t$ such that $(1-t)\\sin \\theta + t \\cdot \\tan \\theta > \\theta$ holds for all $0 < \\t... |
1bc830ed-3c72-4cc3-a9e7-fd4b49fc0c5b | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind positive integers \\(a\\) and \\(b\\) such that \\(a^3 + b = 2^k\\) and \\(b^3 + a = 2^h\\), where \\(h\\) and \\(k\\) are ... |
02461fcb-6cbf-4c5c-bb25-9b6790c46269 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nConsider the function \\( f(x) = f_R(x) + f_I(x) \\), where \\( f_R(x) = 0 \\) if \\( x \\in \\mathbb{Q} \\) and \\( f_I(x) = 1 ... |
b19f068c-51eb-4983-aefc-54bb92e11c91 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven \\( n > 1 \\) different points on a plane, the center of every segment connecting two points is painted pink. What is the ... |
a3320017-8465-48ab-ae8e-ddacfb15c89e | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn triangle \\( \\triangle ABC \\), the points \\( A', B', C' \\) are on sides \\( BC, AC, AB \\) respectively. Also, \\( AA', B... |
34c4b8b3-4530-4fe1-b941-aa4b77f916d1 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet $G$ be a graph on $10$ vertices with degrees $1,1,2,3,3,3,4,4,5,8$. How many paths of length $2$ does $G$ contain?"
},
{... |
b492a2ea-a07f-4982-b807-7579a41e4127 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn acute triangle \\(ABC\\), points \\(P\\), \\(Q\\), and \\(R\\) lie on \\(AB\\), \\(BC\\), and \\(CA\\) respectively such that... |
6b91032f-ffdc-4bdc-a391-b7d104c27876 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSolve the following equations. $4^{\\log _9 x}-6\\cdot 2^{\\log _9x}+2^{\\log _3 27}=0$."
},
{
"role": "assistant",
... |
31c7dba0-43bf-4e83-a5b8-52c0801b3fc9 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn how many ways can a coin be tossed 15 times such that there are no four consecutive tails?"
},
{
"role": "assistant",... |
61cf208e-9d63-4918-bcd2-dbd2823b557d | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\(ABC\\) be an acute-angled triangle. Let \\(P\\) be an arbitrary point inside the triangle, and denote by \\(A_1, B_1, C_1... |
0a386648-b42c-4fd6-be3e-508208e188c0 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn quadrilateral \\(ABCD\\), \\(\\angle BAD = \\angle BCD = 90^\\circ\\). Point \\(E\\) is on \\(AB\\) such that \\(AE = 5\\) an... |
f2d7dcbd-68d4-4c6e-b77b-acf492594fcc | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nEvaluate the definite integral \\( \\int_{\\pi/3}^{\\pi/2} \\frac{\\sqrt[3]{\\sin^3 x - \\sin x}}{\\sin^3 x} \\cot x \\, dx \\).... |
5e7e5e7c-9b29-48a0-b5d4-74fdd0083d3d | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\( A \\) and \\( B \\) be two fixed points, and let there be a circle such that \\( AB \\) is exterior to the circle. Find ... |
1679728e-d733-478b-8a4f-38654f22297e | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn \\( \\triangle XYZ \\), \\( x \\leq y \\leq z \\). If the triangle satisfies \\( \\frac{x^3 + y^3 + z^3}{\\sin^3 X + \\sin^3 ... |
b7736125-2b50-4e0b-8b37-12b324d381d1 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet $\\mathbb{Q^+}$ be the set of positive rational numbers. Let $f: \\mathbb{Q^+} \\to \\mathbb{Q^+}$ be a function that meets ... |
193aa7c0-7cca-4171-b412-4ea206467b83 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the total number of dissimilar terms obtained after the expression $x_1+x_2+x_3+\\ldots +x_n$ has been cubed."
},
{
... |
49bdc024-64b0-4153-acd1-3fe20432e443 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all solutions in $\\mathbb{N}^*$ (positive integers) to the equation $x + y^x = x^y + y$."
},
{
"role": "assistant"... |
af67370e-8975-4651-ad79-1ebe82a76c50 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all positive integers $n$ such that there exists a monic polynomial $P(x)$ of degree $n$ with integer coefficients satisfyi... |
cbefd767-db26-4094-99d8-bb3e7351a429 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\( (x_n)_{n \\ge 1} \\) be a sequence of real numbers such that:\n\\[ x_1 = 2 \\]\n\\[ x_1 + x_2 + \\cdots + x_n = n^2 x_n ... |
8d5a3cf6-467d-4021-b9fe-0f364ce9d005 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhat is the maximum number of squares that can be marked on an $n \\times n$ chessboard such that for any three columns, at most... |
114a4a7a-b8b3-4b32-8bd3-a7db353edd8e | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nPoints \\(A, B,\\) and \\(C\\) lie on the circumference of a unit circle with \\(AB\\) as a diameter. Given that \\(\\frac{|AC|}... |
90245281-181e-47b3-8f5b-972b4d57974b | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhat can you say about the integral \\(\\int_{-1}^{1}\\frac{t^{2n}(1-t^{2})^{2n}}{(1+it)^{3n+1}}dt\\)?"
},
{
"role": "as... |
60031602-826d-4546-bc10-dc19997283d0 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind a conditionally convergent sequence $\\sum a_k$ such that $\\sum |a_k|^c \\cdot \\text{sgn}(a_k)$ diverges for any $c > 0$ ... |
f93717fa-fb97-476f-9986-11ada55beedd | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\(a, b, c\\) be positive real numbers such that \\(a^2 + b^2 + c^2 = 2(ab + bc + ca)\\). Find the minimum value of \\(A = a... |
4d741b27-6bcc-49e6-b4e1-695158d994ab | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nTriangle APM has ∠A = 90° and a perimeter of 152. A circle centered at O (on AP) has a radius of 19 and touches AM at A and PM a... |
45b03b04-78ab-4a6e-b5a8-7d38f38c5990 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the best constant \\( k \\) such that the inequality\n\\[\n\\left(\\frac{a}{b}\\right)^3 + \\left(\\frac{b}{c}\\right)^3 + ... |
a01b727c-2aec-43dd-a663-2a64986cb782 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\( f(x) = \\frac{e^x}{x} \\). Suppose \\( f \\) is infinitely differentiable in \\( (0, \\infty) \\). Find \\( \\lim_{n \\t... |
5411e7d5-36c7-4221-8cde-0214b5020fad | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all polynomials \\( P(x) \\) satisfying the equation:\n\\[ (2x - 1)P(x) = (x - 1)P(2x) \\quad \\forall x \\]"
},
{
... |
c5082702-d884-463f-8ff5-2afd6b21bd5b | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nAdam and Eve decide to produce offspring and continue until they have more boys than girls (they stop if their first child is a ... |
f876e806-9374-4662-ad39-dac807cdc79e | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven the conditions \\(0 < x < 1 < y < 100 < z\\) and the system of equations:\n\\[\n\\log_2 (xyz) = 103\n\\]\n\\[\n\\frac{1}{\... |
655f3825-7ec6-4d08-bfdf-d7a9e1b91ae5 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nEvaluate the integral \\( \\int \\frac{1}{\\sqrt{2+\\sqrt{1+\\sqrt{x}}}} \\,dx \\)."
},
{
"role": "assistant",
"cont... |
c881810e-8bb1-4713-8e03-a60c6d77ee8e | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven a five-digit number \\( m \\), if the middle digit is erased to form a four-digit number \\( n \\), and \\(\\frac{m}{n}\\)... |
0ad51f61-8dca-4afe-b1bb-2d7633961a73 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all continuous functions \\( f: \\mathbb{R} \\to \\mathbb{R} \\) such that for all \\( x \\in \\mathbb{R} \\) and \\( n \\i... |
d4dde6ff-f264-43ac-8cb5-3deb7e0fcf21 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven the recurrence relation $x_{n-1} \\cdot x_{n+1} = 1 - x_{n}$, construct the sequence and determine whether it is periodic,... |
05d27355-0672-4884-ac24-fc6e4abe8ba3 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the limit \\(\\lim_{n\\rightarrow\\infty}\\frac{\\sum_{k=2}^{n}\\left(k^{2}\\cdotp\\sqrt[k]{C_{2k}^{k}}\\right)}{n\\left(n+... |
81b3179e-27c8-4c45-bbdb-0eb9561cb1e4 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind \\(\\lim_{n \\to \\infty} \\frac{\\cos(x^n)}{\\cos(x^{n-1})}\\) for \\(x > 1\\)."
},
{
"role": "assistant",
"co... |
1ae132ce-4d12-47ef-a8d2-0f2764b44297 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all primes \\( p < q < r \\) such that \\( 25pq + r = 2004 \\) and \\( pqr + 1 \\) is a perfect square."
},
{
"role... |
1a3ef32e-fd2a-4005-8e07-e311f667d63f | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA sequence of polyhedra \\( P_i \\) is defined recursively as follows: \\( P_0 \\) is a regular tetrahedron with volume 1. To ob... |
df1bd59a-34a4-42c2-a641-a03832f84117 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSolve for $x$: $\\left|\\frac{6 - 5x}{3 + x}\\right| \\le \\frac{1}{2}$."
},
{
"role": "assistant",
"content": "<thi... |
f10f28d5-786c-40be-a3d9-98e2352999d3 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn the center of a solid sphere, a 6 cm long cylindrical hole is drilled through it. What is the volume that remains?"
},
{
... |
c50f16b3-a130-4280-b70b-db097fdfebef | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhat is the expected number of coin tosses it takes to observe Head followed by two consecutive Tails? (Use the inductive approa... |
272a91f0-da8c-4a0c-a594-ecd4963f97fe | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA circle of radius $R$ passes through the vertices $A$ and $B$ of $\\triangle ABC$ and touches the straight line $AC$ and a poin... |
1ab8467b-8f73-4fcc-ad0e-a6e87e601f93 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all sequences $a_1, a_2, \\ldots, a_{2000}$ of real numbers such that $\\sum_{n=1}^{2000} a_n = 1999$, $\\frac{1}{2} < a_n ... |
ad9cc005-2acc-4d4e-b9f1-1043b692e4cd | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA line segment BC has length 6. Point A is chosen such that ∠BAC is a right angle. For any position of A, a point D is chosen on... |
8e44f570-0966-43ad-a743-6adcc717c25b | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all functions \\( f: \\mathbb{R} \\to \\mathbb{R} \\) such that \n\\[ f(x^2 + f(y)) = y - x^2. \\]"
},
{
"role": "a... |
e7917d14-c190-467c-b5a6-572ddd5c58b1 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn a sequence where the first five numbers are 8, 15, 28, 49, and 80, what is the 9th number?"
},
{
"role": "assistant",... |
f64b9a19-da44-4df7-b855-28c392edd6cf | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\( f(x): [0,1] \\longrightarrow \\mathbb{R} \\) be a continuously differentiable function such that:\n\\[\n\\int_0^1 x f(x)... |
df2c731b-4c50-4559-9edf-6f89905ef159 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all polynomials \\( Q(x) \\) such that the set of values of \\( Q(x) \\) consists of all Fibonacci numbers for integer \\( ... |
0e3cf402-5dfb-4ad2-bf73-d7e442bfcb51 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the fourth roots of \\(-\\frac{1}{2} - \\frac{\\sqrt{3}}{2}i\\)."
},
{
"role": "assistant",
"content": "<think>... |
857c21c7-12a7-45af-8211-8ce73db8ab38 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\(ABC\\) be an equilateral triangle. Let \\(P\\) and \\(Q\\) be points such that points \\(B, P, Q,\\) and \\(C\\) are coll... |
8fab8eb9-e9f0-4383-aa8f-8c04eb7499b4 | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the number of ordered pairs \\((A, B)\\) such that \\(A\\) and \\(B\\) are (not necessarily distinct) subsets of \\(\\{1, 2... |
63387f1c-10e7-4229-8c64-970a5378c6dc | CC BY 4.0 | DeepSeek-R1-0528 | v2 | math | off | [
{
"role": "system",
"content": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\(a\\), \\(b\\), \\(t\\), and \\(k\\) be natural numbers with \\((a, b) = 1\\). What are the conditions on \\(a\\), \\(b\\)... |
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