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Topic: Solving binary quadratic forms
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Randall L. Rathbun

Posts: 62
Registered: 12/6/04
Solving binary quadratic forms
Posted: Nov 23, 2002 8:49 PM
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Does anyone know how to solve (1) quickly

(1) (ax^2 + by^2)(cx^2 + dy^2) = e^2

a,b,c,d,e,x,y are in Z, and gcd(a,b)=1 gcd(c,d)=1

We are given a,b,c & d, and need to find x,y.

Example:

(2) (x^2 + 4248723689280y^2)(5x^2 + 24332920331281y^2) = s^2

We ignore the trivial solution x,y = (0,0)

Randall




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