Is my statement true?

Are all the statements below correct for integer $n$ ?

$n^3-n$ is divisible by $3$ .

$n^5-n$ is divisible by $5$ .

$n^7-n$ is divisible by $7$ .

$n^{11}-n$ is divisible by $11$ .

$n^{13}- n$ is divisible by $13$ .