New types of congruences?

Well these congruences are pretty basic and trivial but I didn't find anything about them in books or on net.

It is interesting to note the following congruences.

$1) \phi(a)^n \equiv \phi(a) \mod a$ Here , $a$ is arbitary prime number and $n$ is any odd number.

$2) \phi(a)^{n'} \equiv 1\mod a$ Here $a$ is any arbitary prime and $n'$ is an arbitary even number.

#NumberTheory

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$