Question: The parameter t in the pair ( (1t) 2 /(1+t) 2 , 2t/(1+t) 2 ) runs through all rational numbers if t = q/p and

The parameter t in the pair ( (1t)2 /(1+t)2 , 2t/(1+t)2) runs through all rational numbers if t = q/p and p, q run through all pairs of integers.

Deduce that if (a, b, c) is any Pythagorean triple then

a/c=(p2-q2)/(p2+q2) , b/c=2pq/(p2+q2) for some integers p and q.

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