On the congruence ax+by = 1 modulo xy

Chalmers University of Technology; Goteborg University); J. Brzezinski (Department of Mathematics; P. Kurlberg (Department of Mathematics; W. Holsztynski

arxiv: math/0308194 · v3 · submitted 2003-08-20 · 🧮 math.NT

On the congruence ax+by = 1 modulo xy

J. Brzezinski (Department of Mathematics , Chalmers University of Technology , Goteborg University) , W. Holsztynski , P. Kurlberg (Department of Mathematics This is my paper

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keywords boundsmodulonumbersolutionscongruencecongruencesdiophantineequation

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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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On the congruence ax+by = 1 modulo xy

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