On the Distribution of Solutions to Linear Equations
نویسندگان
چکیده
Given two relatively prime positive integers m < n we consider the smallest positive solution (x0, y0) to the equation mx−ny = 1. E. I. Dinaburg and Y. G. Sinai have used continued fractions to show that the ratios x0/n are uniformly distributed in [0, 1], when n and m run through consequtive integers of intervals of comparable sizes. We use a bound of exponential sums due to W. Duke, J. B. Friedlander and H. Iwaniec to show a similar result when m and n run through arbitrary sets which are not too thin.
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