Zulip Chat Archive

Stream: FLT-regular

Topic: FLT and the binomial theorem

carlos villacres (Nov 30 2023 at 00:16):

Hello and thank you for your attention, if you read this. I wanted to discuss an interesting polynomial factorization because it is highly relevant. The polynomial factorization is this:

(a+b-c)^n =(c-a)(c-b)g(n) for any n even and

(a+b-c)^n=(a+b)f(n) for any n odd.

What makes this factorization true (and interesting) is that to get this, we assume that a^n+b^n=c^n.

Finally we get a general solution for a,b,c by finding the n'th root of both sides and solving for the appropriate variable.

Thank you if you read this far. Please look here if you're interested, and please ignore if not: https://archive.org/details/fermat-3

Last updated: Dec 20 2023 at 11:08 UTC