Prove that there does not exist any pair (x, y) of positive integers such that: 4xy  x – y is a perfect square.
(In reply to
No Subject by subhobrata)
I noticed a slight problem with your proof.
you state that for (x+y)(x+y1)(xy)^2 to be a perfect
sqaure then (x+y)(x+y1)=0 but a quick counter proof to this
is if (x+y)(x+y1)=20 and xy=4 then you would have
2016=4=2^2
now of course this example does not lead to positive integer x,y solutions, but it does show that your conclusion is not always true. Although I do agree that (x+y)(x+y1) can never be a perfect square

Posted by Daniel
on 20091102 12:33:50 