Prove that 12 | n^2-1 if g.c.d. (n,6)= 1.(adsbygoogle = window.adsbygoogle || []).push({});

I'm pretty sure i already proved this using fermats little theorem, 3 | n^2-1 and 2| n-1, and since n^2-1 is always greater than or equal to 24, (cept for n=1 in which case any number dividies into 0) therefore since 12=2*2*3, 12 | n^2-1

This isn't really atheistically pleasing, can anyone do this a different way?

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# Prove that 12 | n^2-1 if g.c.d. (n,6)= 1.

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