On the congruence ax+by = 1 modulo xy

Details On the congruence ax+by = 1 modulo xy On the congruence ax+by = 1 modulo xy

2003-08-20

arxiv.org/abs/math/0308194v3

Mathematics

Number Theory

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

Scientific paper

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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