prompt list | ground_truth string |
|---|---|
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.2e-3 |
[
{
"content": "Evaluate the integral \\( \\int_0^1 \\frac{3x^4 + 4x^3 + 3x^2}{(4x^3 + 3x^2 + 2x + 1)^2} \\, dx \\).",
"role": "user"
}
] | \dfrac{1}{10} |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\int_{0}^1 nxe^{-nx} \\, dx \\]",
"role": "user"
}
] | 0 |
[
{
"content": "How many distinct squares of elements are there in the alternating group $A_4$?",
"role": "user"
}
] | 9 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.3e-3 N along +z axis |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.98 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.62 mol |
[
{
"content": "Evaluate the differential form \\( \\omega = x^2 dy \\wedge dz + y dx \\wedge dz \\) on the vector fields \\( X = y \\frac{\\partial}{\\partial x} - z \\frac{\\partial}{\\partial y} \\) and \\( Y = z \\frac{\\partial}{\\partial x} + x \\frac{\\partial}{\\partial y} \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the number of solutions \\((\\alpha, \\beta)\\) in the finite field \\(F_{q^2}\\) such that \\(\\alpha + \\alpha^q + \\beta \\beta^q = 0\\).",
"role": "user"
}
] | q^3 |
[
{
"content": "Given a random sample of size \\( n = 72 \\) from a distribution with probability density function \\( f(x) = \\begin{cases} 1/x^2,& 1 < x < \\infty \\\\ 0,&\\text{otherwise} \\end{cases} \\), compute approximately the probability that more than 50 of the observations are less than 3.",
"role"... | 0.266 |
[
{
"content": "Evaluate the finite sum \\( \\frac{1}{n} \\sum_{k=1}^{n-1} \\sin\\left(\\frac{2\\pi k}{n}j\\right) \\) for integers \\( j \\) and \\( n \\), where \\( j < n \\).",
"role": "user"
}
] | 0 |
[
{
"content": "The polynomial $P(x) = 2x^3 + ax^2 + bx + c$ has the property that the mean of its zeros, the product of its zeros, and the sum of the coefficients are all equal. The $y$-intercept of the graph of $y = P(x)$ is 8. What is $b$?",
"role": "user"
}
] | -38 |
[
{
"content": "Let $f,g\\colon\\mathbb{D}^2\\to\\mathbb{C}$ be analytic functions in the bi-disc $\\mathbb{D}^2$ with no common zeros. Determine whether there exist analytic functions $u,v\\colon \\mathbb{D}^2\\to\\mathbb{C}$ such that $uf+vg=1$.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the coefficient of $x^{10}$ in the expansion of $x^3(x^2-3x^3-1)^6$ using the multinomial theorem.",
"role": "user"
}
] | 180 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Basic: $120.93
Dominator: $488.87 |
[
{
"content": "Determine whether the weak-star dual of a Frechet space is quasi-complete.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: \\[ \\lim _{n\\to \\infty}\\frac{e^n\\times n!}{n^n} \\]",
"role": "user"
}
] | \infty |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 310 g of H2O |
[
{
"content": "Evaluate the integral \\( \\int_\\gamma{\\frac{\\log(z+e)}{z}}dz \\), where \\( \\gamma(t)=e^{2it} \\), \\( t\\in[0,\\pi] \\), without using Cauchy's integral formula.",
"role": "user"
}
] | 2\pi i |
[
{
"content": "Evaluate the limit \\(\\lim_{n\\to\\infty}\\left(1+\\frac{1}{\\sqrt{2}}\\right)\\cdots\\left(1+\\frac{1}{\\sqrt{n+1}}\\right)\\).",
"role": "user"
}
] | \infty |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 423.798K |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.0349 T |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $43.90 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 21.06 mJ |
[
{
"content": "Determine the values of $p \\in \\mathbb{R}$ for which the integral \\( \\int_0^\\infty \\frac{\\sin x}{x^p} \\, dx \\) converges.",
"role": "user"
}
] | (0, 2) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Date Description Ref. Debit ($) Credit ($)
31-08-15 Sales 226,700
Sales Discount 2,280
Sales Returns and Allowances 13,000
Income Summary 211,420
(Closing the revenue accounts)
31-08-15 Income Summary 159,850
Cost of goods sold 73,900
Sales salaries expense 32,100
Rent expense-selling space 8,200
St... |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2/7 ohm |
[
{
"content": "Let $f:\\mathbb{R}\\rightarrow\\mathbb{R}$ be a strictly convex continuous function that is differentiable at a point $x_0 \\in \\mathbb{R}$. Is $f$ differentiable on some neighborhood $U$ of $x_0$? Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.67e-4 mol |
[
{
"content": "A thirty-year annuity X has annual payments of $1,000 at the beginning of each year for twelve years, followed by annual payments of $2,000 at the beginning of each year for eighteen years. A perpetuity Y has payments of Q at the end of each year for twenty years, then payments of 3Q at the end of... | 1070.44 |
[
{
"content": "Does a nonempty, quasi-affine variety $Y$ always have an open cover consisting of dense affine subsets? Justify your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 13.10 |
[
{
"content": "Determine the convergence and find the limit of the sequence \\( d_n = \\frac{1}{n^{t+1}} \\sum_{k=1}^n k^t \\) for \\( t > 0 \\).",
"role": "user"
}
] | \dfrac{1}{t + 1} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | expense recognition principle |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\frac{\\sqrt{n^2+3n+1} - \\sqrt{n^2+3n-1}}{\\ln(1+n) - \\ln(2+n)} \\]",
"role": "user"
}
] | -1 |
[
{
"content": "Evaluate the integral: \\[ \\int_{0}^{\\infty}\\frac{\\sin\\left(x^{2}\\right) + \\cos\\left(x^{2}\\right) - 1} {x^{2}}\\,\\mathrm{d}x. \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Given an infinite set $X$, does there exist two distinct sets that are not elements of $X$?",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.4 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 20 m/s^2 |
[
{
"content": "Find \\( \\lim_{n \\rightarrow \\infty} \\mathbb{P}(X_1 + \\ldots + X_n \\leq 0) \\), where the independent binary random variables \\(X_k\\) take values \\(\\pm 1\\) with probabilities \\((1 \\pm k^{-1/2})/2\\) for \\(k = 1, 2, \\ldots\\).",
"role": "user"
}
] | \Phi(-2) |
[
{
"content": "Calculate the limit: \\[ \\lim _{x \\rightarrow \\frac{\\pi}{2}} \\frac{2^{\\cos ^{2} x}-1}{\\ln (\\sin x)} \\]",
"role": "user"
}
] | -2 \ln 2 |
[
{
"content": "The United States Postal Service charges an extra $\\$0.11$ in postage if the length of an envelope, in inches, divided by its height, in inches, is less than $1.3$ or greater than $2.5.$ For how many of these four envelopes must the extra $\\$0.11$ in postage be paid? \\begin{tabular}[t]{ccc}\nEn... | 3 |
[
{
"content": "Let $M$ be a connected topological 2-manifold, i.e., a Hausdorff space locally homeomorphic to $\\mathbb{R}^2$. Suppose $\\pi_1(M)$ is a finitely generated free group. Is $M$ necessarily homeomorphic to a closed surface with finitely many punctures?",
"role": "user"
}
] | Yes |
[
{
"content": "Calculate the contour integral \\( \\int_C \\vec{F}\\cdot\\vec{dr} \\), where \\( \\vec{F}=(y,x) \\) and \\( C \\) is the closed path \\( \\vec{r}(t)=(\\cos t, \\sin t) \\) for \\( 0\\leq t\\leq 2\\pi \\).",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2 mins |
[
{
"content": "Two different 2-digit numbers are randomly chosen and multiplied together. What is the probability that the resulting product is even?",
"role": "user"
}
] | \frac{67}{89} |
[
{
"content": "The diagonals of a rhombus measure 18 feet and 12 feet. What is the perimeter of the rhombus? Express your answer in simplest radical form.",
"role": "user"
}
] | 12\sqrt{13}\text{ feet} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 7.14 m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1090 mL |
[
{
"content": "Let \\( f(t) \\) be the cubic polynomial such that \\( \\cos 3x = f(\\cos x) \\) for all real numbers \\( x \\). Evaluate the integral:\n\\[\n\\int_0^1 \\{f(t)\\}^2 \\sqrt{1-t^2} \\, dt\n\\]",
"role": "user"
}
] | \dfrac{\pi}{8} |
[
{
"content": "Calculate the limit: \\[ \\lim_{n \\to \\infty}(n^2+1)\\cdot(\\ln(n^2-4)-2\\ln(n)) \\]",
"role": "user"
}
] | -4 |
[
{
"content": "Construct an explicit isomorphism between the algebraic group $\\mathbb{G}_m/\\{\\pm 1\\}$ and $\\mathbb{G}_m$.",
"role": "user"
}
] | x \mapsto x^2 |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\rightarrow 0}\\dfrac{1}{x}\\int_x^{2x}e^{-t^2}dt$$",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to 0}\\left[\\frac{1}{\\log (x+ \\sqrt{1+x^2})}-\\frac{1}{\\log (1-x)}\\right] \\]",
"role": "user"
}
] | \infty |
[
{
"content": "Let \\( f: \\mathbb{R} \\to \\mathbb{R} \\) be a differentiable function such that \\( f(x) = f(x/2) + \\frac{x}{2}f'(x) \\). Find the value of \\( f''(20) - f''(10) + 4f''(8) \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the integral \\( \\int_{|z|=1} \\frac{1}{2z - \\sinh(z)} \\, dz \\).",
"role": "user"
}
] | 2\pi i |
[
{
"content": "Let $f: \\mathbb{R}^n \\to \\mathbb{R}$ be a bounded measurable function, and $g: \\mathbb{R} \\to \\mathbb{R}$ be an absolutely continuous function. Determine whether it is true that if $x \\in \\mathbb{R}^n$ is a Lebesgue point of $f$, then $x$ is also a Lebesgue point of $g \\circ f$. Assume th... | True |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $6,125 unfavorable |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 29.42% |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to 0} \\frac{(1+3x)^{1/3}-(1+x)^{1/2}}{x^2}$$",
"role": "user"
}
] | \infty |
[
{
"content": "Consider a Markov chain with parameters $\\alpha,\\beta\\in(0,1)$, where the variables $X_0,X_1,\\dots$ are in the interval $[0,1]$. Given $X_n$, the value of $X_{n+1}$ is either \\[ \\frac{\\alpha X_n}{\\alpha X_n + \\beta (1-X_n)} \\] with probability $\\alpha X_n+\\beta (1-X_n)$, or \\[ \\frac{... | 0.01 |
[
{
"content": "Given 2022 points uniformly distributed on a circle, determine the maximum number of arcs that can be drawn between these points such that no arc is completely included in another, the lengths of arcs are pairwise different, and the smallest and biggest arcs do not overlap or share the same endpoi... | 1011 |
[
{
"content": "Determine whether the following identity holds for every $0 \\leq i \\leq l \\leq r$:\n\\[ \\sum_{j=0}^i\\binom{r-l+i-j}{i-j}\\binom{l-i+j}{j}=\\binom{r+1}{i} \\]",
"role": "user"
}
] | \binom{r+1}{i} |
[
{
"content": "The polynomial \\(x^3 + ax^2 + bx + c\\) has three roots \\(\\alpha \\leq \\beta \\leq \\gamma\\), all of which are positive integers. Given that \\(2^2(a) + 2^1(b) + 2^0(c) = -2^{11}\\), find the sum of all possible values of \\(\\gamma\\).",
"role": "user"
}
] | 6458 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $86.57 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.8 m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 486 THz |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.40 m |
[
{
"content": "The function $f$ takes nonnegative integers to real numbers, such that $f(1) = 1,$ and\n\\[f(m + n) + f(m - n) = \\frac{f(2m) + f(2n)}{2}\\]for all nonnnegative integers $m \\ge n.$ Find the sum of all possible values of $f(10).$",
"role": "user"
}
] | 100 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.01 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | The quantity demanded will increase by 8% while the quantity supplied remains unchanged, leading to a shortage equal to 8% of the equilibrium quantity. |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 79 |
[
{
"content": "Determine whether a Jordan measurable set $X$ is always integrable over any rectangle $R$ that contains it. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the greatest integer less than or equal to the sum \\(\\sum\\limits_{n=1}^{9999} \\frac{1}{n^{\\frac{1}{4}}}\\).",
"role": "user"
}
] | 1332 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -$41,500 |
[
{
"content": "If $A \\cap B$ has a one-to-one correspondence with $A$, and $A \\cup B \\neq A$, does it necessarily follow that $B$ is an infinite set? Answer yes or no and justify your answer.",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.002 m^3 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.6e29 J |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $435 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $35,718.75 |
[
{
"content": "Determine the number of rotational symmetries of a dodecahedron. Consider the symmetries that include the identity rotation, rotations about axes through opposite edges, opposite faces, and opposite vertices. Verify that the total number of rotational symmetries is 60.",
"role": "user"
}
] | 60 |
[
{
"content": "Find the minimum number of distinct non-trivial solutions for the Diophantine equation \\(\\frac{1}{a} = \\frac{1}{x_1} + \\cdots + \\frac{1}{x_n}\\) for any positive integers \\(a\\) and \\(n\\).",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | l=g(T/(2pi))^2 |
[
{
"content": "Let $M$ be a smooth $d$-dimensional oriented Riemannian manifold, and let $p \\in M$. Let $0 \\le k \\le d$ be fixed. Does there exist an open neighborhood $U$ of $p$ that admits a non-zero harmonic $k$-form, i.e., $\\omega \\in \\Omega^k(U)$ satisfying $d\\omega = \\delta \\omega = 0$? Consider t... | Yes |
[
{
"content": "Determine the order of differentiability of the tangent bundle of a $C^2$-manifold. Is the tangent bundle $C^1$, or is it $C^2$?",
"role": "user"
}
] | C^1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.20 K |
[
{
"content": "Find the product of the roots of the equation $18t^2 + 45t -500 =0$.",
"role": "user"
}
] | -\frac{250}{9} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | a = F/m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1126.83 |
[
{
"content": "Evaluate the integral of the function \\( g(x,y) = (x-y)^{2} \\) over the region \\( N \\) defined by the inequalities \\( 0 < x-y < 2 \\) and \\( 0 < x+2y < 3 \\), using an appropriate change of variables.",
"role": "user"
}
] | \dfrac{8}{3} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 56.7 W |
[
{
"content": "Determine if the expression \\((1-5kx^3) \\pmod{25}\\) takes on the values \\(1, 6, 11, 16, 21\\) the same number of times for \\(0 \\leq k \\leq 4\\) and \\(1 \\leq x \\leq 4\\).",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.09 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 42.23 m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1,087,224 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 233 V |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 7.6e+2 kg |
[
{
"content": "Determine the fundamental group of a sphere with two points removed.",
"role": "user"
}
] | \mathbb{Z} |
[
{
"content": "Given the joint density function \\( f(x,y,z) = \\begin{cases} e^{-x-y-z} & \\text{if } x,y,z > 0 \\\\ 0 & \\text{otherwise} \\end{cases} \\), compute the probability \\( P(X < Y < Z) \\).",
"role": "user"
}
] | \dfrac{1}{6} |
[
{
"content": "Determine the constant value that the function \\( f(x) = \\sum_{n=1}^{\\lfloor x \\rfloor} \\left( \\prod_{m=1}^{n} \\left( \\frac{1}{m} \\right) \\right) \\) approaches as \\( x \\) approaches infinity. What is this constant used for?",
"role": "user"
}
] | e - 1 |
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