id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
6,226 |
256 \cdot 256^2 - 255^3 = 195841 = 22^3 + 57^3 = 9^3 + 58^3
|
-2,970 |
7\cdot 11^{\dfrac{1}{2}} = 11^{1 / 2}\cdot (4 + 2(-1) + 5)
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-24,981 |
4\cdot 2.5={10}
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15,609 |
\frac{1}{10^2}*(10 - 2*3)^2 = \frac{1}{10^2}*4^2 = 0.16
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-15,989 |
-\frac{1}{10}*28 = -6*\frac{8}{10} + 10*2/10
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5,998 |
|25\cdot (-1) + x^2| = |(x + 5)\cdot (x + 5\cdot (-1))|
|
-25,799 |
\frac{7}{10 \cdot 2} = \frac{1}{20} \cdot 7
|
1,532 |
\frac{\pi^2}{6} = 1 + 1/4 + 1/9 + \dots
|
30,702 |
f_1 - b - f_2 = -b + f_1 + f_2
|
25,919 |
n^7 - n = n^7 - n^5 + n^5 - n * n^2 + n^3 - n = (n^4 + n^2 + 1)*(n^3 - n)
|
28,190 |
\lambda^2 - a^2 = (-a + \lambda)\cdot (a + \lambda)
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29,998 |
\left(1 - 2x + 3x * x - 4x^3 + \ldots\right)^{\frac12} = \frac{1}{1 + x} = 1 - x + x^2 - x^3 + \ldots
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2,209 |
1 + x^2 - 2x = ((-1) + x)^2
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-9,501 |
-2*2*2*3 y + 2*3*5 = -y*24 + 30
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26,234 |
(1 + n)*(\left(-1\right) + n) + 1 = n^2
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28,768 |
f \cdot x + g_1 \cdot g_2 = f \cdot x + g_1 \cdot g_2
|
-2,188 |
7/12 - \dfrac{1}{12}3 = \frac{1}{12}4
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5,804 |
\sqrt{\left(x + 3\right)\cdot (2 + x)} = \sqrt{x^2 + 5\cdot x + 6}
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31,891 |
|w + z|^2 = (w + z) \left(\bar{w} + \bar{z}\right) = |w|^2 + |z|^2 + w\bar{z} + z\bar{w}
|
421 |
\frac{(-2)\cdot 1/x}{-e^{1/x}\cdot \frac{1}{x \cdot x}} = \dfrac{\left(-2\right)\cdot x}{(-1)\cdot e^{\frac{1}{x}}} = 2\cdot x\cdot e^{-1/x}
|
-1,665 |
\pi/6 + \frac{17}{12}*\pi = \frac{19}{12}*\pi
|
-25,064 |
2/8\cdot 2/7 = 4/56 = \frac{1}{14}
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1,121 |
36 \times \left(-1\right) + t^3 - 10 \times t^2 + 33 \times t = \left(3 \times (-1) + t\right) \times \left(3 \times (-1) + t\right) \times \left(4 \times (-1) + t\right)
|
22,592 |
\sum_{l=1}^\infty \frac{1}{l^3}\cdot l = \sum_{l=1}^\infty \frac{1}{l^2}
|
22,444 |
s^2 + s + 1 = \frac{1}{(-1) + s}*(s^3 + (-1))
|
17,197 |
\alpha^2/(\bar{\alpha}\cdot \alpha) = \frac{\alpha}{\bar{\alpha}}
|
-6,528 |
\frac{3}{2\cdot (7 + c)} = \tfrac{3}{2\cdot c + 14}
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-4,490 |
\frac{1}{z \times z + 2 \times z + 3 \times (-1)} \times (17 \times (-1) + z) = \dfrac{5}{z + 3} - \frac{1}{z + (-1)} \times 4
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-18,306 |
\frac{y \cdot (5 + y)}{\left(y + 6(-1)\right) (y + 5)} = \frac{1}{30 (-1) + y^2 - y}(y \cdot y + y \cdot 5)
|
-606 |
e^{4 \pi i/3*8} = \left(e^{4 \pi i/3}\right)^8
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48,531 |
2 \cdot 2 \cdot 2 + 3^3 = 8 + 27 = 35
|
1,992 |
(a + 1)^2 = \left((-1) + a\right)^2 + a\cdot 4
|
11,509 |
\sin{z^3} \cdot y' + \cos{z^3} \cdot y \cdot z^2 \cdot 3 = \sin{y^3} + 3 \cdot z \cdot y^2 \cdot \cos{y^3} \cdot y'
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8,532 |
1 + 3*n * n - 3*n = -\left((-1) + n\right)^2 * ((-1) + n) + n^3
|
16,958 |
{2 \choose 2} = \frac{1}{2! \times 0!} \times 2! = 1
|
38,680 |
27 = 3^2 3
|
8,866 |
90 = 120*\frac14*3
|
-17,232 |
-\dfrac{56}{9} = -\dfrac{1}{9} \cdot 56
|
-28,887 |
x/6 = x - \tfrac{x}{2} - \dfrac{x}{3}
|
22,602 |
-f^4 + g^4 = (g - f) \cdot (f^3 + g^3 + f \cdot g^2 + f \cdot f \cdot g)
|
8,948 |
g \times g = g \times g
|
-401 |
\pi \cdot 2/3 = \pi \cdot 20/3 - \pi \cdot 6
|
41,111 |
\dfrac{1}{1/2016 + 1}*2017 = 2016
|
-19,713 |
15/8 = 3 \cdot 5/(8)
|
-7,356 |
1/\left(4*4\right) = 1/16
|
-29,427 |
12 \cdot 3/5 = \frac{1}{5} \cdot 36
|
-15,276 |
\dfrac{1}{a^8 \cdot \frac{1}{p^{10}}} \cdot a = \tfrac{1}{\left(\frac{a^4}{p^5}\right)^2 \cdot 1/a}
|
23,383 |
\frac{4}{52} = 3/51*4/52 + \frac{4}{51}*48/52
|
28,301 |
1 - 2 \sin^2(x/2) = \cos(x)
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-9,325 |
32*\left(-1\right) - k*36 = -2*2*3*3*k - 2*2*2*2*2
|
-20,316 |
\frac77 \cdot \dfrac{q + 9}{7 - q} = \frac{q \cdot 7 + 63}{-7 \cdot q + 49}
|
19,068 |
\sec\left(x\right) = -\dfrac{25}{7} \implies -7/25 = \cos(x)
|
27,005 |
(-w + z)*\left(-y + D\right) = z*D - w*D - z*y + y*w
|
12,196 |
\frac18 + \frac18 + \dfrac18*3 = 5/8
|
-20,549 |
z*9/\left(z*9\right)*9/8 = 81 z/(72 z)
|
29,915 |
\sin(z \cdot 8 - z \cdot 5) = \sin{3 \cdot z}
|
6,387 |
-b^2 + c^2 = (b + c)*(-b + c)
|
105 |
(B + A)/G = A/G + B/G
|
14,382 |
2\cdot 5!\cdot 5!/10 = \dfrac{5!}{5}\cdot 5! = 4!\cdot 5!
|
14,279 |
\arccos(\cos{0}) = \arccos(\cos{\pi*2})
|
-521 |
(e^{\frac{5}{4} \cdot \pi \cdot i})^3 = e^{\dfrac{1}{4} \cdot 5 \cdot \pi \cdot i \cdot 3}
|
11,788 |
\sqrt{2} + \left(-1\right) = (1 + \sqrt{2} + (-1) + 3 - \sqrt{2} \cdot 2 + 5 \cdot \sqrt{2} + 7 \cdot \left(-1\right))/4
|
8,886 |
n^2 + n = (n + 1)^2 - 1 + n
|
-4,363 |
\frac{1}{a^3}a^4*56/48 = \frac{56 a^4}{48 a^3}
|
9,536 |
0 = 1 + z + z^2 + ... + z^{r + (-1)} = \frac{z^r + (-1)}{z + (-1)} \Rightarrow z^r = 1
|
30,016 |
\frac{1}{2} \cdot (-\cos(x \cdot 2) + 1) = \sin^2(x)
|
16,186 |
\left(-B = -C + Z*C \Rightarrow C*(-x*f + Z) = -B\right) \Rightarrow \dfrac{1}{-x*f + Z}*((-1)*B) = C
|
10,468 |
det\left(G\right) = det\left(G_{m + (-1)}\right) = 1 \Rightarrow G_{m + (-1)}
|
8,574 |
(y + \omega) \cdot (y + \omega) - y^2 = y\cdot \omega\cdot 2 + \omega^2
|
4,327 |
\sin\left(z\right) = \sin\left(-z + \pi\right)
|
31,022 |
1 + 2 \cdot x = -x \cdot x + (x + 1)^2
|
3,378 |
h_2\cdot h_1 = -h_1\cdot (-h_2)
|
-23,125 |
-\frac{1}{16}*5 = 5/8*(-\dfrac{1}{2})
|
21,618 |
\dfrac{1}{z + \left(-1\right)} \cdot z = \dfrac{1}{z + (-1)} \cdot (z + (-1) + 1) = 1 + \frac{1}{z + (-1)}
|
-11,505 |
-8 + 0\times (-1) - 20\times i = -i\times 20 - 8
|
-23,598 |
2/5\times \frac27 = \frac{4}{35}
|
-2,968 |
\left(9 \cdot 7\right)^{1 / 2} + (25 \cdot 7)^{1 / 2} = 63^{\frac{1}{2}} + 175^{\tfrac{1}{2}}
|
38,973 |
\frac{\pi}{4} \cdot 3 = 2 \cdot \theta rightarrow \theta = 3 \cdot \pi/8
|
19,336 |
x\times g = g\times n' \implies g\times x/g = n'
|
-2,360 |
(-9)^2 = (-9)\cdot \left(-9\right) = 81
|
14,626 |
15 + 3^{2k} = 16 + 9^k - 1^k
|
-11,467 |
-20 + 12*i = 0 + 20*(-1) + 12*i
|
-3,204 |
2^{1 / 2}\cdot 5 + 3\cdot 2^{1 / 2} = 2^{1 / 2}\cdot 25^{\dfrac{1}{2}} + 2^{1 / 2}\cdot 9^{\tfrac{1}{2}}
|
801 |
3 = x^2 + 2 \times x + z^2 \implies z^2 + (x + 1) \times (x + 1) = 4
|
-9,832 |
-2/25 = -\frac{1}{50}*4
|
16,296 |
2^{k - x + 1} \cdot 4^{(-1) + x} = 2^{\left(-1\right) + k + x}
|
11,832 |
(x^2 - 4 \cdot x + 13) \cdot (1 + x) \cdot (x + 2) = x^4 - x^3 + 3 \cdot x^2 + x \cdot 31 + 26
|
13,028 |
0 = t^2 - 2\cdot x\cdot t + 1 \Rightarrow t = x \pm \sqrt{x^2 + \left(-1\right)}
|
1,159 |
2^x \cdot 2^x + 2^x \cdot 2^x = 2 \cdot 2^{2 \cdot x} = 2^{2 \cdot x + 1}
|
15,582 |
1/16 = \frac14 - \frac{3}{16}
|
9,321 |
4^c = (2 \cdot 2)^c = 2^{2\cdot c}
|
21,578 |
(1 + \sin\left(E\right)) (1 + \sin\left(E\right)) + \cos^2\left(E\right) = 1 + 2 \sin\left(E\right) + \sin^2(E) + \cos^2(E) = 2 + 2 \sin\left(E\right)
|
-26,465 |
64 - y \cdot 16 + y \cdot y = y^2 + 8^2 - 2 \cdot 8 \cdot y
|
-23,351 |
\dfrac{1}{49}18 = 3/7*6/7
|
37,383 |
P\left(m\right) = X^m*B = B*X^m
|
26,338 |
0 - 4 = 0 + 4 \cdot (-1)
|
11,175 |
\frac{z + 3\cdot (-1)}{4\cdot (-1) + z} = x \Rightarrow z = \dfrac{4\cdot x + 3\cdot \left(-1\right)}{x + \left(-1\right)}
|
53,340 |
e^\phi = e^\phi
|
-4,439 |
(z + 1)\cdot (z + (-1)) = z^2 + \left(-1\right)
|
36,268 |
\dfrac{1}{\sqrt{1 + m^2}} \cdot m = \frac{1}{\sqrt{z^2 + 1}} \cdot z \Rightarrow \sqrt{1 + z^2} \cdot m = \sqrt{m^2 + 1} \cdot z
|
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