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Which of the following statements is TRUE?

$a^{p-1}\equiv a\;{\rm mod}\; p$, for all integers $a$, and all primes $p>1$.

$a^{p-1}\equiv 1\;{\rm mod}\; p$, for all integers $a$, and all primes $p>1$.

For every integer $a$ coprime to $7$, we have$a^6\equiv a^{12}\;{\rm mod}\;7$.

The set of residues mod $7$ of the numbers $r=1,2,\ldots,6$ is distinct from the set of residuesmod $7$ of the numbers $5r$, $r=1,2,\ldots,6$.

The set of residues mod $10$ of the numbers $r=1,3,7,9$ is distinct from the set of residues mod $10$ ofthe numbers $3r$, $r=1,3,7,9$.