Prove if (a,p)=1, then {a,2a,3a,…,pa} is a complete residue system modulo p.
64453
Prove if $(a,p)=1$, then $\{a,2a,3a,...,pa\}$ is a complete residue system modulo $p$.
114346
Why is $a^{-1}$ mod $p$ equal to $a^{p-2}$ mod $p$?
42376
Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$
68635
When is $2$ a quadratic residue mod $p$?
46147
Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
145041
Given that $p$ is a prime and $p\mid a^n$, prove that $p^n\mid a^n$.
44033
Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$
18108
Show if $(a,p)=1$ there is a unique inverse of $a$ modulo $p$
157884
For any prime $p>3$ show that 3 divides $2p^2+1$
102234
Show $a^p \equiv a \mod 2p$
37093
If p is an odd prime, prove that $1^2 \times 3^2 \times 5^2 \cdots  \times (p-2)^2 \equiv (-1)^{(p+1)/2}\pmod{p}$
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
26478
Show that the congruence $x^{p-1} \equiv 1 \pmod {p^2}$ has precisely $p-1$ solutions modulo $p^2$
64742
Prove a residue matrix $A$ (with coefficients in $\mathbb Z_n)$ has an inverse if and only if $\gcd(\det A,n) = 1$
20161
Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.
101057
Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
84746
elementary proof that infinite primes quadratic residue modulo $p$