On Jun 28, 3:26 am, Andrew Tomazos <and...@tomazos.com> wrote: > On Jun 27, 12:36 pm, Jan Burse <janbu...@fastmail.fm> wrote: > > > > > Andrew Tomazos schrieb: > > > > We can assume that theorems about the nature of integer factorization > > > have previously been established - but which ones specifically would > > > we use to prove your above statements? > > > > I think it would be beneficial if we could compute q, n and m > > > directly. > > > This will result in a multi set of prime > > numbers: > > > z = p1^s1 * ... * pk^sk > > > pi: Some prime number > > si: Some multiplicity > > > Now we can continue working with multi sets. Lets > > assume we have the multi sets for > > > c + a = p1^s1 * ... * pk^sk = q * n * n > > c - a = q1^t1 * ... * qj^sj = q * m * m > > > Then q is the intersection of the two multi sets, > > and the rest follows easily: > > > 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.