DIVISIBILITY CONGRUENCE question

[mathmajor2013]

Question: If gcd(a,42)=1, show that a^6 - 1 is divisible by 168.

Answer: So I know that if 42 were prime, than the Little Fermat Thm says that a^p-1 is congruent to 1 mod p. But I have no idea where to start if p is not prime. Help please.

 

[willem2]

prove the divisibility by 3, 7 and 8 separately. 3 and 7 can be done with Little Fermat's theorem.
For divisibility by 8, factor a^6 -1.