On Jun 28, 3:33 am, Andrew Tomazos <and...@tomazos.com> wrote: > On Jun 28, 3:30 am, Jan Burse <janbu...@fastmail.fm> wrote: > > > Andrew Tomazos schrieb: > > > >> q = intersect(c + a, c - a) > > >> n = sqrt(c + a / q) > > >> m = sqrt(c - a / q) > > > > It's clear that q is an integer, but how do you know that (c + a / q) > > > and (c - a / q) are both perfect squares? That is required if n and m > > > are to be integers. > > > -Andrew. > > > Because of a^2+b^2 = c^2, and the class we assigned > > to m and n. See my first post with a proof attempt.
Isn't q just the GCD of (c + a) and (c - a) ?
It's clear that b*b = (c+a) * (c-a).
It is also clear that the exponents of the prime factorization of (b*b) must all be even.
I am not sure how you conclude from this that ((c+a)/q) and ((c-a)/q) must be perfect squares? Can you express this step formally? -Andrew.