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A problem in Pythagorean Arithmetic

Logic 2018-05-23 v1 Number Theory

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.

Keywords

Cite

@article{arxiv.1510.01645,
  title  = {A problem in Pythagorean Arithmetic},
  author = {Victor Pambuccian},
  journal= {arXiv preprint arXiv:1510.01645},
  year   = {2018}
}
R2 v1 2026-06-22T11:14:03.559Z