instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Evaluate 16*85/272*((-93)/15)/(33/11).\n | -31/3\n | ibivibiv/math_instruct | |
Suppose 16*g - 12*g + 20 = 0. What is the second biggest value in 5, -2/5, g?\n | -2/5\n | ibivibiv/math_instruct | |
What is next in 931, 1877, 2823?\n | 3769\n | ibivibiv/math_instruct | |
What is the next term in 6507, 6518, 6537, 6564, 6599, 6642?\n | 6693\n | ibivibiv/math_instruct | |
Does 1140 divide 30842430?\n | False\n | ibivibiv/math_instruct | |
Which is the nearest to 3/7? (a) -2/9 (b) -4 (c) 7\n | a\n | ibivibiv/math_instruct | |
Let g be ((0 - -4) + 280/(-80))*34. Let l(q) = q**3 - 5*q**2 + 4. Let n be l(5). Suppose 36 = 4*b + n*a, -3*b - 4*a + g = -13. List the prime factors of b.\n | 2, 3\n | ibivibiv/math_instruct | |
In base 13, what is cca + 126?\n | 1123\n | ibivibiv/math_instruct | |
Find l such that -4*l**5/5 + 16*l**4 + 4924*l**3/5 - 6280*l**2 + 5280*l = 0.\n | -30, 0, 1, 5, 44\n | ibivibiv/math_instruct | |
What is the value of -10 + -8 + (-7 - -11) - 7?\n | -21\n | ibivibiv/math_instruct | |
Let j be 2/(-2 - 114/(-58)). Let x be (-188)/j - 3/1. Let g = -163/435 + x. Which is the nearest to -1? (a) g (b) -2/3 (c) 2\n | b\n | ibivibiv/math_instruct | |
Sort 0, -124.73, -0.6.\n | -124.73, -0.6, 0\n | ibivibiv/math_instruct | |
Let u = -61 - 10. Let q = 115 + u. Suppose -h + 2*k + 52 = 6*k, -h - 2*k + q = 0. Does 36 divide h?\n | True\n | ibivibiv/math_instruct | |
Which is the fourth smallest value? (a) 549 (b) 1/6 (c) 0.8 (d) -2/7\n | a\n | ibivibiv/math_instruct | |
Suppose 59 = a + 4*x, -29 = 5*a - 4*x - 348. Let j = -39 + 60. What is the highest common factor of a and j?\n | 21\n | ibivibiv/math_instruct | |
Does 222 divide 253731570?\n | True\n | ibivibiv/math_instruct | |
Suppose 3*r + 2*w - 7*w = 31, -3*r - 2*w - 4 = 0. Solve 6*y - 4 = r*y for y.\n | 1\n | ibivibiv/math_instruct | |
Which is smaller: -0.23 or -183/32?\n | -183/32\n | ibivibiv/math_instruct | |
What is -10614 divided by -183?\n | 58\n | ibivibiv/math_instruct | |
Calculate the remainder when 3715 is divided by 286.\n | 283\n | ibivibiv/math_instruct | |
Solve 5*h + 5 = 3*t, -2*t + 6 = 2*h - 8 for t.\n | 5\n | ibivibiv/math_instruct | |
Let 2*f**4 - 20*f**3 + 72*f**2 - 108*f + 54 = 0. Calculate f.\n | 1, 3\n | ibivibiv/math_instruct | |
Put -34, 4, -1 in decreasing order.\n | 4, -1, -34\n | ibivibiv/math_instruct | |
How many seconds are there in one twentieth of a day?\n | 4320\n | ibivibiv/math_instruct | |
Evaluate (-44)/11*(-25)/20.\n | 5\n | ibivibiv/math_instruct | |
Let r(g) = -43*g. Let s(p) = 2*p**2 - 57*p - 14210. Determine s(r(w)).\n | 3698*w**2 + 2451*w - 14210\n | ibivibiv/math_instruct | |
What is the closest to -0.9 in -18, -1/3, 3?\n | -1/3\n | ibivibiv/math_instruct | |
What is (16/32)/((-10)/(-25))?\n | 5/4\n | ibivibiv/math_instruct | |
Which is the second smallest value? (a) 2 (b) 0.1 (c) -1/32\n | b\n | ibivibiv/math_instruct | |
What is the product of 2.3 and -210?\n | -483\n | ibivibiv/math_instruct | |
Is 34 a factor of 24990?\n | True\n | ibivibiv/math_instruct | |
Calculate the remainder when 1810707 is divided by 218.\n | 217\n | ibivibiv/math_instruct | |
Factor 5*c**2 - 25752990*c + 103011880.\n | 5*(c - 5150594)*(c - 4)\n | ibivibiv/math_instruct | |
Which is the nearest to -1/5? (a) -57 (b) -193 (c) -0.5\n | c\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Definition of limit inferior - paradox
We define the limit inferior and limit superior of a sequence $$(A_n:n\in \mathbb N)$$ of subsets of a set $$X$$ by setting
(1) $$\begin{split}\lim \inf _{n\rightarrow\infty} A_n&=\b... | The concept of limits inferior and superior is fundamental in analysis and sets theory. These concepts allow us to examine the behavior of sequences of sets as we move further along the index. This discussion focuses on the limit inferior and its definition, providing insights into why the given formulation works desp... | ibivibiv/math_instruct | |
What is 353947.1 micrometers in millimeters?\n | 353.9471\n | ibivibiv/math_instruct | |
What are the prime factors of 72674221?\n | 19, 1831, 2089\n | ibivibiv/math_instruct | |
What is the highest common factor of 1068297 and 255?\n | 51\n | ibivibiv/math_instruct | |
Let y = -2565 + 2562. Suppose -2*c - 5*u = -0*c - 84, 4*c - u = 190. Sort c, y, 4.\n | y, 4, c\n | ibivibiv/math_instruct | |
Suppose 4*k + 11 = 4*m + 3, -5*k + 6 = -m. Suppose -2*n = 5*n - 21. Suppose 2*x + 2 - 6 = n*c, 0 = 5*x - 25. Solve -c*s + 15 = 6*i - i, i - m*s = -19 for i.\n | 1\n | ibivibiv/math_instruct | |
What is (-45 - -12) + 14 - -16?\n | -3\n | ibivibiv/math_instruct | |
What is -1069276 rounded to the nearest one thousand?\n | -1069000\n | ibivibiv/math_instruct | |
Suppose 4*j - 543 = -2*t - 43, 4*j + t - 502 = 0. Calculate the greatest common factor of 18 and j.\n | 18\n | ibivibiv/math_instruct | |
Does 9 divide 36379?\n | False\n | ibivibiv/math_instruct | |
Let j(t) = -2*t**2 + 7547*t + 758818. Determine j(-98).\n | 4\n | ibivibiv/math_instruct | |
In base 7, what is -461213 - 23?\n | -461236\n | ibivibiv/math_instruct | |
List the prime factors of 16820.\n | 2, 5, 29\n | ibivibiv/math_instruct | |
Suppose -2*h + 0 = -4*c + 12, -3*h = -5*c + 13. Find the common denominator of 902/495 + 2/c and (10 - 139/10)*10/(-18).\n | 18\n | ibivibiv/math_instruct | |
Let x = -42.1 + -10.9. Let t = x - -54.02. Let d = -0.02 + t. Which is the closest to 1? (a) d (b) -3/2 (c) 2/17\n | a\n | ibivibiv/math_instruct | |
Let 72*l**5 - 428*l**4 + 932*l**3 - 912*l**2 + 400*l - 64 = 0. What is l?\n | 4/9, 1/2, 1, 2\n | ibivibiv/math_instruct | |
Calculate the common denominator of -83/22 and 65/462.\n | 462\n | ibivibiv/math_instruct | |
Collect the terms in 21*m**3 - 46*m**3 - 8*m**3 - 10*m**3.\n | -43*m**3\n | ibivibiv/math_instruct | |
Which is the third smallest value? (a) -0.4 (b) -0.2 (c) 48 (d) -235683\n | b\n | ibivibiv/math_instruct | |
What is 646 minutes before 4:10 PM?\n | 5:24 AM\n | ibivibiv/math_instruct | |
Let g(c) be the third derivative of -c**6/120 + 4*c**5/15 - c**4/12 + 23*c**3/6 - 1099*c**2. Determine g(16).\n | -9\n | ibivibiv/math_instruct | |
Let l = -12776 + 12779. Which is the second biggest value? (a) -4/5 (b) -2 (c) 17 (d) 4 (e) l\n | d\n | ibivibiv/math_instruct | |
Find the second derivative of 52936508*z**5 + 47872921*z + 2 wrt z.\n | 1058730160*z**3\n | ibivibiv/math_instruct | |
What is prob of picking 2 p when two letters picked without replacement from ppppp?\n | 1\n | ibivibiv/math_instruct | |
Let z = 64 - 34. What is the least common multiple of z and (3 + (-45)/10)*-22?\n | 330\n | ibivibiv/math_instruct | |
Suppose -8*l + 18 = -5*l. What is the units digit of l?\n | 6\n | ibivibiv/math_instruct | |
Evaluate -61 + 17 + 82 + -60.\n | -22\n | ibivibiv/math_instruct | |
How many hours are there in seven halves of a day?\n | 84\n | ibivibiv/math_instruct | |
Convert -35a (base 11) to base 2.\n | -110101100\n | ibivibiv/math_instruct | |
Express 3*c + 2*c - 8*c in the form r*c + y and give r.\n | -3\n | ibivibiv/math_instruct | |
-23 + 3080/(-462) + (-4)/3\n | -31\n | ibivibiv/math_instruct | |
Calculate the remainder when 28078859 is divided by 163249.\n | 31\n | ibivibiv/math_instruct | |
Suppose -2*a + 4*c = -52, 0*a - 4*c + 200 = 5*a. Suppose 97 = 5*i + 3*u - a, -5*u - 20 = 0. List the prime factors of i.\n | 29\n | ibivibiv/math_instruct | |
Which is the closest to -1/475? (a) 0.3 (b) 586 (c) 7\n | a\n | ibivibiv/math_instruct | |
What comes next: -28873, -113714, -255109, -453052, -707537, -1018558, -1386109, -1810184?\n | -2290777\n | ibivibiv/math_instruct | |
Calculate -50 divided by -1802.\n | 25/901\n | ibivibiv/math_instruct | |
What comes next: 8, 17, 34, 65, 116, 193?\n | 302\n | ibivibiv/math_instruct | |
(-1)/(-3)*(-2)/(-3)\n | 2/9\n | ibivibiv/math_instruct | |
Which is the nearest to 0.2? (a) -5 (b) 0 (c) 3 (d) -154 (e) 18\n | b\n | ibivibiv/math_instruct | |
What is the closest to 1 in -0.2, -2/5, 0.09, 2?\n | 0.09\n | ibivibiv/math_instruct | |
Suppose -653 = -4*i - 77. Suppose -2*w - 3*h = -9, -w + 1 = -3*h + h. Suppose -w*f + 431 = 2*j, -f + j + i = 2*j. Is f prime?\n | False\n | ibivibiv/math_instruct | |
Let l(r) = -2 + 11*r + 7 - 3 - 1 + 2*r. Let g(y) = 52*y + 4. Calculate -2*g(m) + 9*l(m).\n | 13*m + 1\n | ibivibiv/math_instruct | |
Let b(z) = -z**3 + 4*z**2 + 3*z - 6. Let h = 30 - 26. Calculate b(h).\n | 6\n | ibivibiv/math_instruct | |
Which is smaller: 14193 or 1?\n | 1\n | ibivibiv/math_instruct | |
Simplify ((sqrt(684)*3 + sqrt(684))**2 - (sqrt(95)/sqrt(5) + 2)) + (1 + sqrt(1216))**2*4*-6.\n | -18266 - 385*sqrt(19)\n | ibivibiv/math_instruct | |
What is 176 minutes after 11:05 AM?\n | 2:01 PM\n | ibivibiv/math_instruct | |
Suppose 4*f = 2*f - 10, -2*o = 5*f + 21. Factor 4/3*y + 4/9*y**4 - 4/3*y**3 + 4/9*y**o - 8/9.\n | 4*(y - 2)*(y - 1)**2*(y + 1)/9\n | ibivibiv/math_instruct | |
Factor -3*l**2/5 - 60943086*l/5 + 60943089/5.\n | -3*(l - 1)*(l + 20314363)/5\n | ibivibiv/math_instruct | |
Is 1099800 a multiple of 312?\n | True\n | ibivibiv/math_instruct | |
Let t be 6/(-20)*20/(-15). Which is the nearest to t? (a) 3 (b) -0.5 (c) -0.3\n | c\n | ibivibiv/math_instruct | |
Sort -3, -220, 13, 6, 3 in decreasing order.\n | 13, 6, 3, -3, -220\n | ibivibiv/math_instruct | |
What comes next: 322, 1701, 3992, 7189, 11286?\n | 16277\n | ibivibiv/math_instruct | |
Calculate the remainder when 21235 is divided by 2735.\n | 2090\n | ibivibiv/math_instruct | |
Let g = 6.3 + -1.3. Let y = -0.98 + -0.02. What is the closest to 0 in y, -2, g?\n | y\n | ibivibiv/math_instruct | |
Rearrange ((-3*t + 3*t - 5*t**2)*(4 + 0 - 3) - 13 + 13 - 7*t**2)*(32*t - 30*t + 54*t) to the form i*t**3 + o*t + l*t**2 + k and give l.\n | 0\n | ibivibiv/math_instruct | |
Let x(s) = s**3 + 12*s**2 - 17*s + 785. Calculate the remainder when x(-16) is divided by 21.\n | 12\n | ibivibiv/math_instruct | |
Suppose -2*u + 14 - 2 = 0. Suppose 5*y + 4*o - 8 = 0, 2*y + u = 4*y + 3*o. Suppose 3*d + y*d = 6. Solve 15 = -5*s + d*n, -2*s - 5*n = -2*n - 13 for s.\n | -1\n | ibivibiv/math_instruct | |
Solve -2/9*p**3 + 4/3 - 4/3*p**2 + 2/9*p = 0.\n | -6, -1, 1\n | ibivibiv/math_instruct | |
What is the second smallest value in 332, 0.5, -5/2?\n | 0.5\n | ibivibiv/math_instruct | |
Let x = -2 - -4. Suppose 3 = -5*v + 3*s, -v = x*v + 3*s - 3. Suppose -18 = -2*o - v*o. List the prime factors of o.\n | 3\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"Prove that $n^k+1$ has a prime divisor $>2k$
Let $$n\ge3$$ & $$k\ge2$$. Show that $$n^k +1$$ has a prime divisor $$>2k$$.
• Where did you find this problem? It's quite interesting. – Carl Schildkraut Oct 20 '18 at 17:12
By... | This mathematical statement is an application of Zsigmondy's theorem, which deals with primality conditions in certain arithmetic sequences. Before diving into the details of the problem, let us first establish some definitions and background knowledge.
**Prime number:** A natural number greater than 1 that cannot be... | ibivibiv/math_instruct | |
In base 4, what is -302101 - -10232?\n | -231203\n | ibivibiv/math_instruct | |
Express (-5 + 5 - 2*b)*(2 + 6*b - 2) in the form j*b + x + d*b**2 and give d.\n | -12\n | ibivibiv/math_instruct | |
Let j(i) = 3*i**2 - 3*i - i**2 + 0*i**2 - 4*i**2 - 4 - i**3. Suppose 3*m - 7 = 2*x, 0*x - 2*x - 3*m = -23. What is the remainder when j(-3) is divided by x?\n | 2\n | ibivibiv/math_instruct | |
What is the hundreds digit of 378?\n | 3\n | ibivibiv/math_instruct | |
Simplify (3*sqrt(68)*-3*-3)**2.\n | 49572\n | ibivibiv/math_instruct |
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