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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

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wheretogo

Posts: 5
Registered: 10/7/10
Re: About a diophante equation x^2+y^2=a^2+b^2
Posted: Oct 7, 2010 7:01 AM
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> 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



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