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Modular hyperbolas

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Japanese Journal of Mathematics Aims and scope

Abstract

We give a survey of a variety of recent results about the distribution and some geometric properties of points (x, y) on modular hyperbolas \({xy \equiv a\;(\mod m)}\). We also outline a very diverse range of applications of such results, discuss multivariate generalisations and suggest a number of open problems of different levels of difficulty.

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    Igor E. Shparlinski

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Shparlinski, I.E. Modular hyperbolas. Jpn. J. Math. 7, 235–294 (2012). https://doi.org/10.1007/s11537-012-1140-8

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