Linear congruences with ratios

Shparlinski, Igor

doi:10.1090/proc/12949

Linear congruences with ratios
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by Igor E. Shparlinski

Proc. Amer. Math. Soc. 144 (2016), 2837-2846

DOI: https://doi.org/10.1090/proc/12949

Published electronically: January 20, 2016

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Abstract:

We use new bounds of double exponential sums with ratios of integers from prescribed intervals to get an asymptotic formula for the number of solutions to congruences \[ \sum _{j=1}^n a_j \frac {x_j}{y_j} \equiv a_0 \pmod p, \] with variables from rather general sets.

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