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I have to prove that sentence, but I'm not sure how to do that. Help!

Thomas Andrews
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Arcarida
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  • Hint: $p\equiv 0,1,2,3,4,5 \bmod 6$. Are all residues possible? What happens with $p\pm1$? – lhf Oct 14 '21 at 23:33

2 Answers2

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The only thing we have to prove now is that the prime cannot be 3 mod 6.

If it is 3 mod 6, then it is divisible by 3. Only leaves you with 1 and 5 mod 6.

Note: 1 and 5 mod 6 are the p-1 and p+1, respectively.

The fact is relied upon that all primes greater than 3 are odd.

Aaa Lol_dude
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$p+1 $ and $p-1$ are both even and one of $p-1, p, p+1$ is a multiple of $3$ but of course it cannot be $p$ itself. So $p-1$ or $p+1$ is divisible by $2$ and $3$.

Anonmath101
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