On the congruence $x^x\equiv λ\pmod p$

Javier Cilleruelo; Moubariz Z. Garaev

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arXiv · 1503.02730

On the congruence $x^x\equiv λ\pmod p$

Javier Cilleruelo·Moubariz Z. Garaev

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Abstract

In the present paper we obtain several new results related to the problem of upper bound estimates for the number of solutions of the congruence $$ x^{x}\equiv λ\pmod p;\quad x\in \mathbb{N},\quad x\le p-1, $$ where $p$ is a large prime number, $λ$ is an integer corpime to $p$. Our arguments are based on recent estimates of trigonometric sums over subgroups due to Shkredov and Shteinikov.

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BibTeX RIS

Javier Cilleruelo, Moubariz Z. Garaev. 2015-03-09. On the congruence $x^x\equiv λ\pmod p$. https://arxiv.org/abs/1503.02730

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