Considering just positive integers, there are 6 factorizations of 495 into two factors:

1*495, 3*165, 5*99, 9*55, 11*45 and 15*33. Each of these corresponds to one of

the six (x,y) pairs bobbym listed in post #4. For example: 1*495=248^2-247^2 and

24^2-9^2 = (24+9)(24-9) = 33*15.

In general for an odd composite number each of its unique factorizations (other than a perfect

square factorization) corresponds to a difference of squares. For 9 = 1*9 we get 5^2-4^2

= (5+4)(5-4) = 9*1 but 3*3 has no difference of squares representation unless we allow zero:

3^2-0^2 = (3+0)(3-0) = 3*3.

But we were talking about POSITIVE integers.

If M is an odd composite number and M=n*m where n and m are different, we get

as a difference of squares factorization.

If I recall correctly this was involved in one of Fermat's methods of factoring odd composites.

Have a grrreeeeaaaaaaat day!