Any divisor of $(n + 1)^p - n^p$ is $1 \textrm{ mod } p$
113763
Let $p$,$\ q$ be prime numbers and $n\in \mathbb{N}$ such that $p \nmid n-1$. If $p \mid n^q-1$, then $q \mid p-1$.
52530
There exists a prime congruent to $m$ mod $p$
100255
If a prime divides the hypotenuse of a primitive Pythagorean triple, then $p \equiv 1$ (mod 4)
96062
Show $\underbrace{{111\cdots}1}_{{\small{p-1} \ 1's}}$ is divisible by $p$
122577
Prove that $(n^3 - 1)n^3(n^3 + 1)$ is divisible by $504$
44033
Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$
114346
Why is $a^{-1}$ mod $p$ equal to $a^{p-2}$ mod $p$?
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
120627
Reducibility of polynomials modulo p
15314
Number of solutions to $x^n \equiv 1 \mod p$
36941
If $p$ is congruent to $2 \pmod 3$, how can I prove that all $a$, $1 \le a \le p-1$ are cubic residues $\mod p$?
10266
Minimal polynomial reducible modulo every prime $p$
74898
$1^n +2^n + \cdots +(p-1)^n \mod p =$?
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
104484
Prove that $r$ is a primitive root modulo $p$ if and only if $r^{(p−1)/q}\not\equiv 1\pmod{p}$
146851
Prove that $-3$ is a quadratic residue mod an odd prime $>3$ if and only if $p$ is of the form of $6n+1$
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$