Prove that $(a+b)^p$ = $a^p+b^p \bmod p$ for any prime $p$
32762
Proof for: $(a+b)^{p} \equiv a^p + b^p \pmod p$
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too
75528
$x^2-x+1$ has a root $\!\bmod p\,$ for infinitely many primes $p$
110703
How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
17601
How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
61860
Show that if $a$ has order $3\bmod p$ then $a+1$ has order $6\bmod p$.
64453
Prove if $(a,p)=1$, then $\{a,2a,3a,...,pa\}$ is a complete residue system modulo $p$.
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 $a=b$
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
87397
Show that $a^2 \bmod b = (a \bmod b)^2 \bmod b$
94017
If p is a prime and a ∈Z. How do we prove that the congruence x^x ≡ a (mod p) is solvable?
21629
Using Fermat's Little Theorem Prove if $p$ is prime, prove $1^p + 2^p + 3^p +...+(p-1)^p \equiv 0 \bmod{p}$
158161
$\mathbb{Q}(\sqrt p_{1}+\sqrt p_{2})=\mathbb{Q}(\sqrt p_{1},\sqrt p_{2})$ for $p_{1},p_{2}$ primes.
18714
$\gcd\left(a+b,\frac{a^p+b^p}{a+b}\right)=1$, or $p$
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
42677
Proving $(\alpha + \beta)^{p^n} = \alpha^{p^n} + \beta^{p^n}$ in a finite field
52461
Why does $(g^b \bmod m)^a \bmod m = (g^a \bmod m)^b \bmod m$?