Number theory: $(a + b)^p ≡ a^p + b^p\pmod{p}$
32762
Proof for: $(a+b)^{p} \equiv a^p + b^p \pmod p$
21874
Solve $x^3+x \equiv 1 \pmod p$
34323
Prove that $a^{(p-1)/2} \equiv 1$ (mod p) and $a^{(p-1)/2} \equiv -1 \pmod p$
38727
Modular Exponentiation and Primes
3109
Prove that $(p+q)^m \leq p^m+q^m$
126280
In a P.I.D., if $a^m = b^m$ and $a^n = b^n$ for $m, n \in \mathbb{N}$ with $\gcd(m,n) = 1$, then $a=b$
114346
Why is $a^{-1}$ mod $p$ equal to $a^{p-2}$ mod $p$?
65826
Find a prime number $p$ and an integer $b<p$ such that $p$ divides $b^{p−1}−1$.
121717
Prove that $z^2 \equiv ab\pmod p$ is solvable if and only if both or neither of $x^2 \equiv a \pmod p$, $x^2 \equiv b \pmod p$ are solvable.
38876
$r! \equiv (−1)^k \pmod p$
6160
How to prove a number $a$ is quadratic residue modulo $n$?
360
Modular exponentiation by hand ($a^b\bmod c$)
60305
Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$
17601
How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
64453
Prove if $(a,p)=1$, then $\{a,2a,3a,...,pa\}$ is a complete residue system modulo $p$.
104484
Prove that $r$ is a primitive root modulo $p$ if and only if $r^{(p−1)/q}\not\equiv 1\pmod{p}$
88036
Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$