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Dozen Divisibility Dilemma (Posted on 2010-12-02) Difficulty: 3 of 5
Each of x and y is a positive integer such that: x2 5y2 = 1.

Prove that x*y is always divisible by 12.

No Solution Yet Submitted by K Sengupta    
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re(2): Possible solution Comment 4 of 4 |
(In reply to re: Possible solution by Harry)

Thanks!

I wasn't sure if the extra step was needed. Indeed the stronger solve integer 4n-5y^2=1 also produces no integer solutions; I'll add something to my earlier post to round off the proof.

Edited on December 4, 2010, 12:31 am
  Posted by broll on 2010-12-04 00:15:06

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