Calculate the remainder when a(12) is divided by 13.
9
Let y be 72/20*(-10)/(-6). Suppose 0 = -t + y*t - 10. Suppose 0 = -q + j + 51, -5*q - j = t*j - 239. What is the remainder when q is divided by 13?
10
Suppose 0 = -d - 3*x - 4, -4*d - 9 = -4*x - 57. Calculate the remainder when 125 is divided by d.
5
Suppose -994 + 328 = -37*w. Calculate the remainder when 69 is divided by w.
15
Let j be 14/63 + 101/(-9). Let v(d) = d**3 - 6*d**2 - 3*d - 4. Let l be v(7). Let m = j + l. What is the remainder when 38 is divided by m?
12
Suppose 6 = -9*o + 12*o. Suppose o*k = k + 29. What is the remainder when k is divided by 15?
14
Suppose 12 = -u - 5*n, -2*u - 15*n + 18*n + 28 = 0. Calculate the remainder when 19 is divided by u.
3
Let g(c) = c**3 + 10*c**2 + 6*c + 10. Suppose 0 = -45*s + 49*s + 36. Calculate the remainder when g(s) is divided by 10.
7
Suppose -270 = 10*f - 7*f. What is the remainder when 69 is divided by (324/f)/((-3)/20)?
21
Let z(x) = 6*x**3 - x**2. Let m be z(1). Let a(t) = 3*t + 7. Let r be a(m). Let h = -11 + r. Calculate the remainder when 31 is divided by h.
9
Suppose -2*o + 186 = 62. Suppose y + 4 = 6. Let z(j) = 3*j**3 - 4*j + 5. Calculate the remainder when o is divided by z(y).
20
Suppose -2*k + 0*k + 112 = 0. Suppose 0 = 3*r - f - 44, -1 = f - 2. What is the remainder when k is divided by r?
11
Let p = 2416 - 2358. What is the remainder when 341 is divided by p?
51
Calculate the remainder when (-236)/(-3) - 1/(-3) is divided by (8/((-112)/(-231)))/(6/8).
13
Let n be ((-608)/(-20))/4*-10. Let r = 51 + n. Let k = -5 - r. Calculate the remainder when 77 is divided by k.
17
Let l(q) be the third derivative of q**5/60 - q**4/6 + 2*q**3/3 - 7*q**2. Let v be l(-5). Suppose 9 = -k + v. Calculate the remainder when k is divided by 11.
7
Suppose 0 = -5*o - 4*u - 1, 3*o - 4*o - u = 1. Suppose 2*b - 106 = -4*s, -o + 47 = s - 3*b. Suppose 1 = -4*w + s. What is the remainder when w is divided by 2?
1
Suppose 25 = 5*f - 10. Let k(x) = x**2 - f*x + 0 + 2*x + 2*x - 1. Calculate the remainder when 35 is divided by k(5).
8
Suppose 2*n + 2 = -4*x, 5*n + 3*x - 31 = 5*x. Suppose -n*o + 3 + 87 = 0. Calculate the remainder when 51 is divided by o.
15
Suppose 0 = 4*s - 2*c - 225 - 313, 2*s = 4*c + 272. What is the remainder when s is divided by 23?
19
Let n(b) = b**2 - 4*b + 6. Let m be n(2). Calculate the remainder when m/6 + (-58)/(-6) is divided by 5.
0
Suppose 0 = -13*w + 31 + 398. Let c = -6 + 15. What is the remainder when w is divided by c?
6
Let z(y) = 56 + y**2 - 9 + 6. Let u = -1 - -1. Calculate the remainder when z(u) is divided by 27.
26
Suppose -6*i = -4*i + 92. Let m = 52 + i. What is the remainder when 19 is divided by m?
1
Let c(f) = -f**2 + 10*f + 8. What is the remainder when 279 is divided by c(10)?
7
Suppose 0 = 5*t - 4*c - 159, -110 - 19 = -4*t + 5*c. Calculate the remainder when t is divided by 8.
7
Let o = 376 - 305. What is the remainder when o is divided by 39?
32
Suppose 118 + 80 = 22*v. Let l(b) = -b**3 + b + 3. Let z be l(0). Suppose y + 2*y - 3*a - 39 = 0, v = 3*y + z*a. What is the remainder when 37 is divided by y?
5
Suppose -o = -2 - 0, 2*o = 2*k. Suppose l = 3*l - j, 0 = -j + 2. Suppose -w + l = -3. Calculate the remainder when w is divided by k.
0
Let o = 444 - 354. What is the remainder when 1076 is divided by o?
86
Let v(y) = -y**3 + 14*y**2 - 10*y - 2. Let m be v(13). Suppose -m = -7*t + 26. What is the remainder when t is divided by 5?
4
Let y(z) = -z**2 + 3*z + 20. Let v be y(6). Suppose -7*i + 65 = -v*i. Calculate the remainder when 50 is divided by i.
11
Suppose 21*y - 48 = 15*y. Calculate the remainder when 347 is divided by y.
3
Suppose -h = 4*t - 1139, -t + 3*h = -143 - 158. What is the remainder when t is divided by 12?
10
Let b = 197 + -186. What is the remainder when 13 is divided by b?
2
Let x = -8 - -16. Let t(u) = -4*u - 14. Let w(c) = 3*c + 9. Let q(o) = -5*t(o) - 7*w(o). Calculate the remainder when x is divided by q(3).
0
Suppose -c = 5*o - 3*o + 2, -4*c - 18 = 3*o. Let y = c + 13. Calculate the remainder when ((1 - 0) + -2)*(-5 + -15) is divided by y.
6
Let s = 40 - 26. Suppose -4*a + 0*a = 16. Calculate the remainder when -91*a*(-1)/(-14) is divided by s.
12
Let m = 2 + 2. Let s be m/(-24) - (-13)/6. Suppose s*o - 6 - 40 = -5*f, 2*o - 6 = 0. What is the remainder when 14 is divided by f?
6
Suppose x + 160 = -0*f + 4*f, -20 = 5*x. Suppose -3*l + 4*l - f = 0. What is the remainder when 151 is divided by l?
34
Let m(c) = c**3 - c**2 + 6*c + 3. Suppose 78 = 27*f - 21*f. What is the remainder when m(6) is divided by f?
11
Suppose 3*f + 2*z = 6*f - 242, -3*z + 157 = 2*f. Suppose -q - 44 = -3*q. What is the remainder when f is divided by q?
14
Suppose 2*y + 186 = -4*y. Let t = y + 37. Calculate the remainder when t is divided by (0 - -4) + (-4)/4.
0
Let j be ((-192)/(-2 + -2))/1. Suppose 0 = -3*v + j - 3. Suppose 3*p - 2*p - 5 = 0. What is the remainder when v is divided by p?
0
Suppose 0 = -24*a + 26*a - 2494. Calculate the remainder when a is divided by 32.
31
Let t(j) = j**3 - 6*j**2 + 6*j - 18. Let p be t(7). Let x = 137 - p. Calculate the remainder when x is divided by 20.
4
Suppose -3*t - 2*t + 3 = -3*y, -3*y + 9 = -t. Let k be (-2 + 6)*1/2. Suppose 22 = k*a + 6. Calculate the remainder when a is divided by t.
2
Let q(v) = v**3 + 19*v**2 + 14*v + 40. Calculate the remainder when q(-18) is divided by 19.
17
Let m(i) = i**2 + 35*i + 227. What is the remainder when 150 is divided by m(-28)?
26
Suppose -5*b - 2 = 3. What is the remainder when -23*2/2*b is divided by (4/10)/((-1)/(-30))?
11
Suppose -17 - 1 = -6*u. Suppose o = r - u, -r + 11 = r - o. Calculate the remainder when 37 is divided by r.
5
Let m be 0/(-1 - (3 + -3)). Suppose 2*n - 2*i = m, 2*n - i = 3*n - 4. Calculate the remainder when (372/8)/(n/4) is divided by 24.
21
Let l be -3*(2 + (-2)/2). Let b be (-39)/((-2)/2) + l. Suppose -3*i + 115 = -2*c, -3*i = -5*c + b - 139. What is the remainder when i is divided by 14?
13
Let i(j) = 3*j**3 - 2*j**2 - 2*j + 1. Let g = -159 + 240. Let s = -51 + g. Calculate the remainder when i(3) is divided by s.
28
Let o be (7 + (-27)/6)*8/(-10). What is the remainder when 27 is divided by (8/10)/(o/(-35))?
13
Calculate the remainder when (3 - -3)/(9/78) is divided by (6 - 9)*(-11)/3.
8
Suppose m = 3*c - 221, 5*c - m + 5*m - 340 = 0. What is the remainder when c is divided by 40?
32
Suppose -4*q + 918 = -4*z + 3*z, 0 = q - 4*z - 222. Calculate the remainder when q is divided by 47.
42
Let p(y) = -y**3 - 22*y**2 - 59*y - 37. Calculate the remainder when 12 is divided by p(-19).
0
Suppose 4*p + 4*i = 300, 3*p - 4*i + 10 = 235. Let f = p + -3. Suppose -5*v + 111 = -14. Calculate the remainder when f is divided by v.
22
Let d = 334 + -287. What is the remainder when 134 is divided by d?
40
Suppose 3*m = 89 - 2. Calculate the remainder when ((-4)/3)/(4/(-342)) is divided by m.
27
Suppose 6 = -3*y, 5*q + y + 2*y - 649 = 0. What is the remainder when 2095 is divided by q?
130
Suppose -12 = -2*g - 52. What is the remainder when 8/g + (2 - 861/(-15)) is divided by 12?
11
Calculate the remainder when 127 is divided by 5 - -1 - 32/(-4).
1
Let b be ((-525)/(-100))/(1/((-8)/2)). Let h(u) = u**3 + 21*u**2 - 3*u + 22. What is the remainder when h(b) is divided by 13?
7
Let h = 142 + -81. Let x = -14 + h. What is the remainder when x is divided by 12?
11
Let h = -5 - -9. Suppose 14 = h*j + d + d, -4*d - 8 = -j. Let z(w) = w**2 + 4*w - 2. Calculate the remainder when j is divided by z(-5).
1
Suppose -1094 - 1018 = -12*q. Calculate the remainder when q is divided by 12.
8
Let w be 8/3 + (-2)/(-6). Suppose -v = -w*o - 9, -4*v - 2*o - 6 = -0*v. Suppose v = -y - 0*y + 60. What is the remainder when y is divided by 21?
18
Let n be (12/8)/(3 + (-198)/64). Let x(o) = -5*o + 17. Calculate the remainder when x(n) is divided by 14.
13
Let q = 48 + -59. Let w = 29 + q. What is the remainder when w is divided by 12?
6
Suppose -l - 9 = 3*a, 0*l + 3*a + 21 = l. Suppose 3*s = -5 + 17. Suppose y - s = 6. Calculate the remainder when y is divided by l.
4
Let t be (-200)/(-56) - (-3)/7. Let j(x) = -x**3 + 4*x**2 - x + 7. What is the remainder when 11 is divided by j(t)?
2
Let l(x) = -x**2 - 14*x - 25. Let g be l(-7). Suppose 0 = -0*a - a 