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/P^{2} + B/Q^{2} = 1

Prove that these are the only quadruplets that exist.

(In reply to

Possible solution by broll)

Broll:

How did you solve (a*(q-p)(q+p))/(q^2-21)=p^2?

Not real clear (or simple) to me.