Show that $37|333^{777} + 777^{333}$
50247
Compute the period of a decimal number a priori
49967
Find the last two digits of $ 7^{81} ?$
60073
Proving $4(a^3 + b^3) \ge (a + b)^3$ and $9(a^3 + b^3 + c^3) \ge (a + b + c)^3$
20504
$\forall m,n \in \Bbb N$ : $\ 56786730\mid mn(m^{60}-n^{60})$
17194
$6^{(n+2)} + 7^{(2n+1)}$ is divisible by $43$ for $n \ge 1$
24444
Prove that $371\cdots 1$ is not prime
149508
Prove $9^n \equiv 9 \pmod{24}\quad \forall n \in \Bbb N^*$
64668
Verify that $4(29!)+5!$ is divisible by $31$.
12210
Show that $a^{61} \equiv a\pmod{1001}$ for every $a \in \mathbb{N}$
117167
$3^{n+1}$ divides $2^{3^n}+1$
61582
Find the remainder of $\frac{2^{2014}}{7}$
43940
Showing that $n$ is pseudoprime to the base $a$
7491
How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?
42289
prove that there are infinitely many numbers of the form $x = 111....1$ such that $31\mid x$
5358
How to prove that 2017 divides $1^{2017}+2^{2017}+\dots+2017^{2017}$?
127833
Proving that $7^n(3n+1)-1$ is divisible by 9
118018
Show $ (n+1)^{1/3}-n^{1/3}=O\left(n^{-2/3}\right) $