by hemangsarkar, Oct 19, 2012, 4:05 AM
Q) find all positive integer solutions to
my take on it
or

this must have integer roots. we consider a quadratic in x.
the roots will be
so we get
so,

= perfect square.
so

= perfect square. now we can clearly see that by bezout's identity
so,

and

are relatively prime.
so they both must be perfect squares.
. but quadratic residues modulo

are
.
i think that pretty much does it.
if you find some mistake, let me know.
This post has been edited 1 time. Last edited by hemangsarkar, Oct 19, 2012, 12:23 PM