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 $ax+by \equiv 1$ modulo $xy$.
Publié le : 2005-05-14
Classification:
Diophantine equation,
linear congruence,
divisor function,
11D45,
11A25,
11D72
@article{1136926970,
author = {Brzezi\'nski, J. and Holszty\'nski, W. and Kurlberg, P.},
title = {On the Congruence $\boldsymbol{ax+by \equiv 1}$ Modulo $\boldsymbol{xy}$},
journal = {Experiment. Math.},
volume = {14},
number = {1},
year = {2005},
pages = { 391-401},
language = {en},
url = {http://dml.mathdoc.fr/item/1136926970}
}
Brzeziński, J.; Holsztyński, W.; Kurlberg, P. On the Congruence $\boldsymbol{ax+by \equiv 1}$ Modulo $\boldsymbol{xy}$. Experiment. Math., Tome 14 (2005) no. 1, pp. 391-401. http://gdmltest.u-ga.fr/item/1136926970/