Let $p$ be prime. Prove if $p|(a^p - b^p)$, then $p^2 | (a^p - b^p)$
13478
Prove that if $a^p-b^p$ is divisible by $p$, then it is also divisible by $p^2$
344
Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.
84603
Prove that if $p$ is a prime such that $p^2+2$ is a prime then $p=3$.
36943
How to prove that $L=${$a^p$: p is prime} isn't regular?
127816
Number theory proof mod p
94917
Prove that for every prime $p$, there exists a solution to $(x^2-2)(x^2-6)(x^2-3) \equiv 0 \mod(p)$
130653
$p^2$ divides $ab$ and $\gcd(a,b)=1$. Show $p^2$ divides $a$ or $p^2$ divides $b$
107502
Let $p \geq 2$. Prove that if $2^p-1$ is prime then $p$ must also be prime.
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
33714
$p$ prime, $p\mid a^k \Rightarrow p^k\mid a^k$
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
65826
Find a prime number $p$ and an integer $b<p$ such that $p$ divides $b^{p−1}−1$.
137511
Trying to show that $\sup \{b^p:p\in Q,\;0<p<x\} = \inf\{b^q:q\in Q,\;x<q\}$
52249
Is it true that $||a|^p - |b|^p| \le C_p|a - b|^p$ for $1 < p < \infty$?
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
64654
Suppose $a, b$ and $n$ are positive integers. Prove that $a^n$ divides $b^n$ if and only if $a$ divides $b$.
95162
For a odd prime $p, \exists a,b$ such that $a^2 + ab + b^2 \equiv 0 \pmod{p} \iff \exists x,y $ such taht $x^2 + xy + y^2 = p$?