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1 Answer
- rodolfo riverolLv 66 years ago
You can use Fermat's little theorem to show:
p^4 = 1 mod 5, which implies p^8 = 1 mod 5
p^2 = 1 mod 3 which implies p^8 = 1 mod 3
Since p is an odd prime then p^2 - 1 = (2k+1)^2 - 1 = 4k(k+1) = 0 mod 8, which implies p^8 = 1 mod 8.
Since 3, 5, and 8 are pairwise relatively prime and p^8 - 1 is divisible by each of them then by Euclid p^8 - 1 is divisible by their product = 30.
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