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
SN - 0029-4527
VL - 59
SP - 197
EP - 204
JO - Notre Dame Journal of Formal Logic
JF - Notre Dame Journal of Formal Logic
IS - 2
ER -