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Exponential Sums and Congruences with Factorials

Moubariz Z. Garaev·Florian Luca·Igor E. Shparlinski
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Abstract

We estimate the number of solutions of certain diagonal congruences involving factorials. We use these results to bound exponential sums with products of two factorials $n!m!$ and also derive asymptotic formulas for the number of solutions of various congruences with factorials. For example, we prove that the products of two factorials $n!m!$ with $\max\{n,m\} ..., n_{49}\} < p^{8775/8794+ ε}$.

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BibTeXRIS

Moubariz Z. Garaev, Florian Luca, Igor E. Shparlinski. 2004-03-24. Exponential Sums and Congruences with Factorials. https://arxiv.org/abs/math/0403424

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