perplexus.info :: Numbers : Sweet 17

Home > Numbers

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

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

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

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info