Experimental Mathematics

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

J. Brzeziński, W. Holsztyński, and P. Kurlberg

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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

Permanent link to this document
https://projecteuclid.org/euclid.em/1136926970

Mathematical Reviews number (MathSciNet)
MR2193402

Zentralblatt MATH identifier
1152.11322

Subjects
Primary: 11D45: Counting solutions of Diophantine equations
Secondary: 11A25: Arithmetic functions; related numbers; inversion formulas 11D72: Equations in many variables [See also 11P55]

Keywords
Diophantine equation linear congruence divisor function

Citation

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


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