## Experimental Mathematics

### On the Congruence $\boldsymbol{ax+by \equiv 1}$ Modulo $\boldsymbol{xy}$

#### 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 $ax+by \equiv 1$ modulo $xy$.

#### Article information

Source
Experiment. Math., Volume 14, Issue 4 (2005), 391-401.

Dates
First available in Project Euclid: 10 January 2006

Brzeziński, J.; Holsztyński, W.; Kurlberg, P. On the Congruence $\boldsymbol{ax+by \equiv 1}$ Modulo $\boldsymbol{xy}$. Experiment. Math. 14 (2005), no. 4, 391--401. https://projecteuclid.org/euclid.em/1136926970