Prove that $ (p-1)! +1 \equiv 0 \mod p$
2218
Prove that $(n-1)! \equiv -1 \pmod{n}$ iff $n$ is prime [Wilson's Theorem]
14724
For primes $p≡3\pmod 4$, prove that $[(p−1)/2]!≡±1\pmod p$.
22962
How to show $\binom{2p}{p} \equiv 2\pmod p$?
29231
Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
138941
If p $\equiv$ 3 (mod 4) with p prime, prove -1 is a non-quadratic residue modulo p.
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
21629
Using Fermat's Little Theorem Prove if $p$ is prime, prove $1^p + 2^p + 3^p +...+(p-1)^p \equiv 0 \bmod{p}$
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
18108
Show if $(a,p)=1$ there is a unique inverse of $a$ modulo $p$
17601
How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
108237
Show $a^p \equiv b^p \mod p^2$
100558
Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
52530
There exists a prime congruent to $m$ mod $p$
71788
Prove existence of multiplicative inverse modulo p when p is prime
7448
Prove $S \doteq \sum_{n=1}^{\infty} p_n  0$ assuming $0 \leq p_n < 1$.
6332
If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined