On the congruence ax+by = 1 modulo xy
Number Theory
2009-09-29 v3
Abstract
We give bounds on the number of solutions to the Diophantine equation (X+1/x)(Y+1/y) = n as n tends to infinity. These bounds are related to the number of solutions to congruences of the form ax+by = 1 modulo xy.
Cite
@article{arxiv.math/0308194,
title = {On the congruence ax+by = 1 modulo xy},
author = {J. Brzezinski and W. Holsztynski and P. Kurlberg},
journal= {arXiv preprint arXiv:math/0308194},
year = {2009}
}
Comments
LaTeX2e, 10 pages with 1 figure. Results in section 6 improved (upper bound on the average number of solutions given). Author list changed. Submitted