If $a ≡ b$ (mod $n$), prove that $a^5 ≡ b^5$ (mod $n$)
10105
Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
19459
Find remainder of $F_n$ when divided by $5$
20161
Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.
29231
Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
36602
$a^m=b^m$ and $a^n=b^n$ imply $a=b$
18693
If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$
53915
prove that $a \equiv b \mod m$ is an equivalence relation on the integers
133382
Proof that $a+b+\frac{1}{1+\sqrt{ab}}\geq\frac{5}{2}$
21108
Perfect squares and modularly congruency in mod 5
46147
Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
153313
Prove that for all integers $ a $ and $ b $, if $ a $ divides $ b $, then $ a^{2} $ divides $ b^{2} $.
52032
Prove that ${n^5 - n}$ is divisible by 5
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
90438
To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$
146053
Proving identities (mod $pq$) using Fermat's little theorem?
134885
proving that $\mathbb{Q}(\sqrt{5}, \sqrt{6}) = \mathbb{Q}(\sqrt{5}+ \sqrt{6}) $