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Experimental Mathematics Volume 14, 2005 - Issue 4
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Original Article

On the Congruence ax + by = 1 Modulo xy

J. Brzeziński Department of Mathematics, Chalmers University of Technology and Göteborg University, S–41296 Göteborg, Sweden
,
W. Holsztyński 400 E. Remington Dr, #D233 Sunnyvale, CA 94087
&
P. Kurlberg Department of Mathematics, Royal Institute of Technology, S–10044 Stockholm, Sweden
Pages 391-401 | Published online: 30 Jan 2011
 
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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 = 1 modulo xy.

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