Notre Dame Journal of Formal Logic

A Problem in Pythagorean Arithmetic

Victor Pambuccian

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.

Article information

Source
Notre Dame J. Formal Logic, Volume 59, Number 2 (2018), 197-204.

Dates
Accepted: 2 December 2015
First available in Project Euclid: 9 January 2018

https://projecteuclid.org/euclid.ndjfl/1515467280

Digital Object Identifier
doi:10.1215/00294527-2017-0028

Mathematical Reviews number (MathSciNet)
MR3778307

Zentralblatt MATH identifier
06870288

Citation

Pambuccian, Victor. A Problem in Pythagorean Arithmetic. Notre Dame J. Formal Logic 59 (2018), no. 2, 197--204. doi:10.1215/00294527-2017-0028. https://projecteuclid.org/euclid.ndjfl/1515467280

References

• [1] Kaye, R., Models of Peano Arithmetic, vol. 15 of Oxford Logic Guides, Oxford University Press, Oxford, 1991.
• [2] Menn S., and V. Pambuccian, “Addenda et corrigenda to ‘The arithmetic of the even and the odd’,” Review of Symbolic Logic, vol. 9 (2016), pp. 638–40.
• [3] Pambuccian, V. “The arithmetic of the even and the odd,” Review of Symbolic Logic, vol. 9 (2016), pp. 359–69.
• [4] Schacht, C. “Another arithmetic of the even and the odd,” Review of Symbolic Logic, submitted.