I have managed to show that $(a + b)^p \equiv a^p + b^p \pmod p$, $a$ and $b$ being any integer and $p$ any prime.
How can I prove from this that $a^p \equiv a \pmod p$?
I have managed to show that $(a + b)^p \equiv a^p + b^p \pmod p$, $a$ and $b$ being any integer and $p$ any prime.
How can I prove from this that $a^p \equiv a \pmod p$?