How to Prove a^5 ≡ a (mod 15) for Any Integer a?

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Homework Statement


Prove that a5 [tex]\equiv[/tex]a (mod 15) for every integer a.


Homework Equations





The Attempt at a Solution


I do not know how to show a5-a is divisible by 15
 

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[tex]a^5 - a = (a-1)a(a+1)(a^2 + 1)[/tex] can you show that this expression is divisible by 3 and by 5 individually? This would imply it's divisible by 15.
 

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