Find three integers $n_1, n_2, n_3$ such that $n_1^3 + n_2^3 + n_3^3 = 42$
103274
Integer solutions to the equation $a^3+b^3+c^3=30$
56624
Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers
144779
The number of ways to represent $(n^2+n)/4$ as a sum of $n/2$ distinct integers in $1,\dots,n$
33757
For what natural numbers is $n^3 < 2^n$? Prove by induction
145287
Solve for integers $x, y, z$ such that $x + y = 1 - z$ and $x^3 + y^3 = 1 - z^2$.
116054
The number $(3+\sqrt{5})^n+(3-\sqrt{5})^n$ is an integer
128306
Show that for all $n ∈ Z$, $2n^3 + 3n^2 + n$ is divisible by both 2 and 3.
61871
Formula for the $n$th term of $1, 2, 2, 3, 3, 3, 4, 4 ,4, 4, 5, ...$
16176
Primitive Pythagorean triple divisible by 3
157186
Finding integers satisfying $m^2 - n^2 = 1111$
100336
Find an integer having the remainders $2,3,4,5$ when divided by $3,4,5,6$, respectively.
137652
How many solutions does the equation $n_1 + n_2 + n_3 + n_4 + n_5 = 20$ have in the positive integers if $n_1 < n_2 < n_3 < n_4 < n_5$?
136459
Prove ${n - 1 \choose k - 1} + {n - 2 \choose k - 1} + {n - 3 \choose k - 1} + \dots + {k - 1 \choose k - 1} = {n \choose k}$
85297
find a $3 \times 3$ matrix $A$ such that $A \neq I_3$ and $A^{197}=I_3$.
122096
Find $GCD(n^2+1,n+1)$
122891
integer as sum of three binomials
22084
$\mathbb{Z}[i] / (2+3i)$ has 13 elements