The congruence $a^p+b^p\equiv 1\;(\text{mod}\;p^2)$
10191
Binomial theorem: divisibility by $n^2$
127901
If $x^2+y^2 \equiv 0\pmod{p}$, then $p \equiv 1 \pmod{4}$
13904
$p = x^2 + xy + y^2$ if and only if $p \equiv 1 \text{ mod }3$?
34430
Why does $(\frac{p-1}{2}!)^2 = (-1)^{\frac{p+1}{2}}$ mod $p$?
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
38876
$r! \equiv (−1)^k \pmod p$
126725
If $p$ is prime and $p$ $\equiv$ $1$ (mod 4), then the congruence $x^2$ $\equiv$ $-1$ (mod $p$) has two incongruent solutions...
46429
Question about proof that $(a + b)^p = a^p+b^p$ in a field of characteristic $p$.
44033
Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$
61825
Congruence class $[a]$ modulo $m$, $\gcd(x, m) = \gcd(a, m)$
96237
$1^2 + 2^2 + 3^2 + \cdots + (n-1)^2 \equiv 0$ mod n iff $n \equiv \pm 1$ mod 6
144851
For a prime $p \equiv 1$ or $3$ (mod $8$), show that the equation $x^{2} + 2y^{2} = p$ has a solution.
42780
Show that if $a^{n-1} \equiv 1 \pmod{n}$ for all $a$ such that $\gcd(n,a) = 1$, then $a^{n} \equiv a \pmod{n}$ for all $a$.
53915
prove that $a \equiv b \mod m$ is an equivalence relation on the integers
29231
Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
45882
Solving a congruence without Fermat's little theorem
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.