Euler's theorem - $a^{x}≡a^{x \text{ mod} \varphi(n)} \text{ (mod n)}$
4972
Mod of numbers with large exponents [modular order reduction]
137175
Fermat's little theorem proof by Euler
34323
Prove that $a^{(p-1)/2} \equiv 1$ (mod p) and $a^{(p-1)/2} \equiv -1 \pmod p$
8784
modulo version of the quadratic formula and Euler's criterion
46147
Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
10105
Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
128634
Doubt related to a theorem in congruences of Chapter 5 of Apostol Introduction to analytic number theory
154933
Prove $(p-k)!(k-1)!\equiv (-1)^k \text{ mod p }$
19071
solution set for congruence $x^2 \equiv 1 \mod m$
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
73238
Show that $a^{q-1} \equiv 1 \pmod{pq}$
82878
Order of cyclic groups and the Euler phi function
90537
Converse of Fermat's Little Theorem.
49938
Proof of $a^{\phi (n) +1} \equiv a \pmod{\! n} $ Carmichael generalization of Fermat-Euler's theorem.
142788
Can't use Euler's Theorem?
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.