### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 197-204 |

Number of pages | 8 |

Journal | Notre Dame Journal of Formal Logic |

Volume | 59 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2018 |

### Fingerprint

### Keywords

- Elementary number theory
- Pythagorean arithmetic

### ASJC Scopus subject areas

- Logic

### Cite this

**Problem in pythagorean arithmetic.** / Pambuccian, Victor.

Research output: Contribution to journal › Article

*Notre Dame Journal of Formal Logic*, vol. 59, no. 2, pp. 197-204. https://doi.org/10.1215/00294527-2017-0028

}

TY - JOUR

T1 - Problem in pythagorean arithmetic

AU - Pambuccian, Victor

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Elementary number theory

KW - Pythagorean arithmetic

UR - http://www.scopus.com/inward/record.url?scp=85044831843&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044831843&partnerID=8YFLogxK

U2 - 10.1215/00294527-2017-0028

DO - 10.1215/00294527-2017-0028

M3 - Article

AN - SCOPUS:85044831843

VL - 59

SP - 197

EP - 204

JO - Notre Dame Journal of Formal Logic

JF - Notre Dame Journal of Formal Logic

SN - 0029-4527

IS - 2

ER -