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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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re(2): Two unhelpful(?) observations | Comment 3 of 8 |
(In reply to re: Two unhelpful(?) observations by broll)

Well, I believe I proved my observation, but it is not true that the observation rules out solutions.

For instance, (1,2) is a solution.
The gcd(4x+1,4y-1) = gcd(5,7) = 1
and x+y = 3 divides 16xy+1=33

Also, per my observation,
x+y = 3 divides both 5*3 and 9*7

  Posted by Steve Herman on 2015-05-10 08:40:43
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