Suppose a number N can be written as P times Q times R times..., where all of P, Q, R... can each be written as the sum of two perfect nonzero squares.
Show that in this case N itself can also be written as the sum of two perfect squares.
It is sufficient to prove this for N=P*Q because then
N=P*R*S can be simplified by letting Q=P*S which has been proven.
let P = (a^2 + b^2) and Q = (c^2 + d^2) with a>b>0 and d>c>0
P*Q = a^2c^2 + a^2d^2 + b^2c^2 + b^2d^2
= (ac + bd)^2 + (ad - bc)^2
Posted by Jer
on 2007-05-18 13:03:28