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Sweet 17 (Posted on 2011-09-05)

Let x be any positive integer greater than 1 , which is not divisible by 17.

Prove that either x^8-1, or x^8+1, is divisible by 17.

See The Solution Submitted by broll

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More generally (spoiler)

| Comment 2 of 3 |

For any odd prime p (ie, p =2n+1), it is true that

2^p = 2 mod p (Fermat's little theorem)

2^2n = 1 mod p

2^n = +/- 1 mod p

Posted by Steve Herman on 2011-09-05 12:24:12

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