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Positive Pair Poser (Posted on 2015-05-09) Difficulty: 3 of 5
Determine all possible pairs (x,y) of positive integers with gcd(4x+1, 4y-1) = 1 such that x+y divides 16xy+1

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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No Subject | Comment 7 of 8 |
Steve Herman, I plead guilty to a little hand-waving on your 1) but Harry takes care of the question nicely. 

As to your 2), you're correct.  My statement about (x+y) = 1 mod 16 is just wrong.  What I should have written is that (x+y) is odd because it factors the odd integer 16xy+1.

Harry, thanks for your explanatory post.

  Posted by xdog on 2015-05-11 10:35:21
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