Determine all possible quadruplets (A, B, P, Q) of positive integers, with P ≤ Q, that satisfy this system of equations:

A + B = 21, and:

A/P² + B/Q² = 1

Prove that these are the only quadruplets that exist.

(In reply to re: Possible solution by Steve Herman)

Steve,

I'm afraid that's all the work I did on it (apart from some jottings on equalities of the form w/x^2+y/z^2=1) Once I got to the formula I gave, it seemed obvious that there could only be those answers, so I didn't explore further.

Posted by broll on 2011-01-18 01:57:24