## Notre Dame Journal of Formal Logic

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

### A Problem in Pythagorean Arithmetic

#### 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**

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