2014/12/03 by Mike Winkler, Winkler, Mike, Fillipi, Andreas
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1412.1689
openalex publication_date 2014/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a short proof of an algebraic identity. For integers n≥ 2 and variables x,y,z, it represents (xn+yn-zn) as a value of the quadratic form \mathcal A2+\mathcal B2-\mathcal C2 after multiplication by an explicit factor. Consequently, any hypothetical solution of xn+yn=zn yields a Pythagorean triple (\mathcal A,\mathcal B,\mathcal C) consisting of explicit polynomial expressions in x,y,z.