Prove that if $a^{170} ≡ 1 \text{ (mod n) and }a^{111} ≡ 1 \text{ (mod n)} \text{ then } a ≡ 1 \text{ (mod n)}$
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
87397
Show that $a^2 \bmod b = (a \bmod b)^2 \bmod b$
110752
$g^\frac{p-1}{2} \equiv -1 \ (mod \ p)$
18108
Show if $(a,p)=1$ there is a unique inverse of $a$ modulo $p$
106584
If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
114346
Why is $a^{-1}$ mod $p$ equal to $a^{p-2}$ mod $p$?
46780
Proving $((a\bmod n) (b\bmod n))\bmod n = ab\bmod n $
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
360
Modular exponentiation by hand ($a^b\bmod c$)
6332
If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined
121706
Show $\text{det}(A)$ is divisible by $2^{n-1}$
146053
Proving identities (mod $pq$) using Fermat's little theorem?
68705
Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
62996
A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.
125868
Prove $a \equiv b \pmod{c} \implies a^n \equiv b^n \pmod{c}$.