Noob question about an exponential congruence

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When is this congruence true for integer $a>1$?

$$(a-1)^{(a+1)} \equiv (a-1) \> mod \> (a^2-1)$$

My try:

$$(a-1)^{a} \equiv \> 1 \> mod \> (a+1)(a-1)$$

I do not know what to do now.

Thank you.