On the congruence ax+by = 1 modulo xy

2003/08/20 by J. Brzezinski, Juliusz Brzeziński, W. Holsztynski +5
Mathematics · #11A25 #11D45 (Primary) #11D75 (Secondary) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT) #math.NT #msc:11A25 #msc:11D45 #msc:11D75

paper · pdf · doi:10.48550/arxiv.math/0308194

LaTeX2e, 10 pages with 1 figure. Results in section 6 improved (upper bound on the average number of solutions given). Author list changed. Submitted

openalex publication_date 2003/08/20 · arxiv created 2003/12/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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