A problem in Pythagorean Arithmetic (1510.01645v1)

Published 4 Oct 2015 in math.LO and math.NT

Abstract: Problem 2 at the 56th International Mathematical Olympiad (2015) asks for all triples (a,b,c) of positive integers for which ab-c, bc-a, and ca-b are all powers of 2. We show that this problem requires only a primitive form of arithmetic, going back to the Pythagoreans, which is the arithmetic of the even and the odd.