Question 1026519
<pre>
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:

{{{system(x^2-y^2=5,2xy=12,x^2+y^2=13)}}}

Adding the first and third equations:

{{{2x^2=18}}}

{{{x^2=9}}}

{{{x=3}}}

Substituting x² = 9

{{{x^2+y^2=13}}}

{{{9+y^2=13}}}

{{{y^2=4}}}

{{{y=2}}}

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

Answer: c

Edwin</pre>