A Mean Value Theorem for the Diophantine Equation axy-x-y=n

2011/07/30 by Jing-Jing Huang, Huang, Jing-Jing
Mathematics · #11D45 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11D45

paper · pdf · doi:10.48550/arxiv.1108.0095

11 pages, to appear in Acta Math. Hungar. A couple of typos are corrected in the new version

arxiv created 2011/08/14 · arxiv updated 2011/08/16

Abstract

In this paper, we prove an asymptotic formula for the average number of solutions to the Diophantine equation axy-x-y=n in which a is fixed and and n varies.

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