solve x^2 - y^2 = 2764 for integer x and y > 0

x^2 - y^2 = (x + y)(x - y) = 2764
 so both (x + y) and (x - y) are factors of 2764.

x+ y and x- y both are even or odd ( as one even and on odd shall  give fractions)

 as product is even so x + y and x-y both are even

Now factorize 2764 into product of primes: 2764 = 4*691 = 2*2*691

so x+ y= 1382 and x- y =2 => x = 692 and y =690 is the only solution