Notre Dame Journal of Formal Logic

A Problem in Pythagorean Arithmetic

Victor Pambuccian

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Abstract

Problem 2 at the 56th International Mathematical Olympiad (2015) asks for all triples (a,b,c) of positive integers for which abc, bca, and cab 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
Received: 22 October 2015
Accepted: 2 December 2015
First available in Project Euclid: 9 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1515467280

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

Mathematical Reviews number (MathSciNet)
MR3778307

Zentralblatt MATH identifier
06870288

Subjects
Primary: 03C62: Models of arithmetic and set theory [See also 03Hxx] 11U99: None of the above, but in this section
Secondary: 11A99: None of the above, but in this section

Keywords
Pythagorean arithmetic elementary number theory

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


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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.