Here is a simple example of how to calculate the two distinct Pythagorean

triples for a product of two primes.

If you can relate your method of finding the distinct Pythagorean

triples to

this method, perhaps we together will have found a new relationship.

65 = 5 * 13

5 = 2**2 + 1**2

13 = 3**2 + 2**2

(2 + i)*(3 - 2 i)

= (2 * 3 + 2 * 2) + (1*3 - 2 * 2) i

= 8 - i

65 = 8**2 + 1**2

(2 + i) * (3 + 2 i)

= (2 * 3 - 2 * 1) + (2 * 2 + 3 * 1)

= 4 + 7 i

65 = 4**2 + 7**2