Problem 2 at the 56th International Mathematical Olympiad (2015) asks for all triples of positive integers for which , , and are all powers of . 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.
"A Problem in Pythagorean Arithmetic." Notre Dame J. Formal Logic 59 (2) 197 - 204, 2018. https://doi.org/10.1215/00294527-2017-0028