Solve in $\mathbb N$: $ 2^x\equiv 1 \bmod{x}$
107448
proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$
29231
Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
53042
Find solutions to $\varphi\left(n\right)=2^{32}$
125057
How do I solve a problem with term $a^{n} + b^{n}$?
61860
Show that if $a$ has order $3\bmod p$ then $a+1$ has order $6\bmod p$.
10105
Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
38849
Solve $x^y \, = \, y^x$
101057
Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
102234
Show $a^p \equiv a \mod 2p$
360
Modular exponentiation by hand ($a^b\bmod c$)
4435
What does $\!\bmod(n,x^r-1)$ mean? [in AKS primality test]
36611
Algorithms for solving the discrete logarithm $a^x \equiv b\pmod{n}$ when $\gcd(a,n) \neq 1$
131941
Solve quadratic congruences.
34154
Prove the statement $\forall x\in\mathbb N (x > 1\to\exists k\in\mathbb N\exists m \in\mathbb N (m \equiv 1 (\text{mod }2) \wedge x = 2^km))$.
26301
Prove that $x^3 \equiv x \bmod 6$ for all integers $x$
51153
Number of solutions to $x^2\equiv a\pmod m$
87304
Solving for $x$ : $a^x+b^x=c$