On the congruence x^x≡ λ\pmod p

2015/03/09 by Javier Cilleruelo, Cilleruelo, Javier, Moubariz Z. Garaev +1
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · doi:10.48550/arxiv.1503.02730

openalex publication_date 2015/03/09 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

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≡ λ\pmod p; x∈ ℕ, x≤ 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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