The Pythagorean triples are generated by x,y and

(x²-y²,2xy,x²+y²) where x > y > 0, x,y both integers.

To generate (5,12,13), we have the over-determined system:



Adding the first and third equations:







Substituting x² = 9









And if we check we find that x=3, y=2 
satisfies all three equations of the
over-determined system above.

Answer: c

Edwin