Determine all possible pairs (x,y) of positive integers with gcd(4x+1, 4y-1) = 1 such that x+y divides 16xy+1

(In reply to Two unhelpful(?) observations by Steve Herman)

I'm not sure about your observation, but if true it is sufficient to show that there are no solutions, the reason being that those are just the solutions where (4x+1) and (4y-1) can have terms with common divisors.

Edited on May 10, 2015, 8:11 am

Posted by broll on 2015-05-10 08:08:17