Prove that $n^{31} \equiv n$ mod $77$ for all integers $n$
12210
Show that $a^{61} \equiv a\pmod{1001}$ for every $a \in \mathbb{N}$
46400
how do i prove that $17^n-12^n-24^n+19^n \equiv 0 \pmod{35}$
56464
Proving the irrationality of $e^n$
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
78416
Show that $7$ divides $a^{15}-a^3$ for any integer $a$
26301
Prove that $x^3 \equiv x \bmod 6$ for all integers $x$
123482
How to compute $\mathbb{Z}_n^*$, the unit group of the integers modulo $n$?
42780
Show that if $a^{n-1} \equiv 1 \pmod{n}$ for all $a$ such that $\gcd(n,a) = 1$, then $a^{n} \equiv a \pmod{n}$ for all $a$.
51221
Is $x^3-9$ irreducible over the integers mod 31?
29231
Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
57654
Congruent Modulo $n$: definition
95061
Proving that $2^{2\cdot 3^{n-1}}\equiv 1+3^n\pmod{3^{n+1}}$ for every natural $n$
134450
Chinese Remainder Theorem $\ x\equiv m_k-2\pmod{m_k}$
28957
Verifying that $2^{44}-1$ is divisible by $89$
15314
Number of solutions to $x^n \equiv 1 \mod p$
105225
Number Theory: Complete set of residues modulo $n$
90438
To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$