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Topic:
About a diophante equation x^2+y^2=a^2+b^2
Replies:
5
Last Post:
Oct 7, 2010 2:51 PM




Re: About a diophante equation x^2+y^2=a^2+b^2
Posted:
Oct 7, 2010 7:01 AM


> It is not hard to prove that the folowing formula > gives a solution : > > x = mp +nq > y = mq  np > a = mq + np > b = mp  nq > for m,n,p,q any positifve integer with n < m and p < > q > (by developing) > > This is due to Fibonacci (1225) I know it.
> It is harder to prove that *all* solutions are given > by this formula.
I want to find all integral solutions (x,y) of the equation with a, b given and GCD(x,y)=1. Thank you your answer



