TY - JOUR

T1 - Problem in pythagorean arithmetic

AU - Pambuccian, Victor

N1 - Publisher Copyright:
© 2018 by University of Notre Dame.

PY - 2018

Y1 - 2018

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 -