Proving that $a^{25}$ mod 65 = $a$ mod 65
49938
Proof of $a^{\phi (n) +1} \equiv a \pmod{\! n} $ Carmichael generalization of Fermat-Euler's theorem.
65873
A proof for Atiyah-Macdonald Exercise I.21.iii
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
13317
show that $a^{12} \equiv 1 \mod 32760$ for each $a \in \mathbb{Z}$ such that $\text{gcd}(a, 32760) = 1$
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
94017
If p is a prime and a ∈Z. How do we prove that the congruence x^x ≡ a (mod p) is solvable?
46147
Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
10105
Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
29231
Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
84733
Why $a\equiv b\pmod n$ implies $a$ and $b$ have equal remainder when divided by $n$?
31917
If $q$ is coprime to $a$ then $a\mid nq-1,\,$ so $q$ is invertible mod $a$
34192
Solve $x^{5} \equiv 2$ mod $221\ $ [Taking modular $k$'th roots if unique]
91565
How to efficiently compute $\,25^{37}\pmod{55}$?
118981
Proving $\sqrt{ab} = \sqrt a\sqrt b$
94855
Prove if a (mod n) has a multiplicative inverse, then it's unique