Prove that for ANY integer n, has no prime divisors of the form 6m-1.

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Attempt:

Let p be a prime divisor of .

Then ≡ 0 (mod p)

=> ≡ 0 (mod p)

=> ≡ 1 (mod p)

Let = order of n mod p

=> |3

=> = 1 or 3

Now I'm stuck here. How to finish the proof from here?

Any help is greatly appreciated!

[also under discussion in math links forum]