Let a+b=p, where a and b are positive integer numbers and p is a prime. Prove that $a^p+b^p$ is divisible by $p^2$, but it is not divisible by $p^3$!
Let a+b=p, where a and b are positive integer numbers and p is a prime. Prove that $a^p+b^p$ is divisible by $p^2$, but it is not divisible by $p^3$!
$a^p+b^p=\left(a+b\right)^p-\sum_{k=1}^{p-1}{p \choose k}a^{p-k}b^k$, start with that.