The congruence $x^{x}\equiv \lambda \pmod p$

DOI10.1090/proc/12919zbMath1415.11006arXiv1503.02730OpenAlexW2963804143MaRDI QIDQ2796710

Javier Cilleruelo, Moubariz Z. Garaev

Publication date: 29 March 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.02730

zbMATH Keywords

upper bound estimatesnumber of solutions of congruence

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Congruences; primitive roots; residue systems (11A07)

Related Items (4)

Statistics for fixed points of the self-power map ⋮ On distribution of elements of subgroups in arithmetic progressions modulo a prime ⋮ On the few products, many sums problem ⋮ Counting fixed points and rooted closed walks of the singular map \(x \mapsto x^{x^n}\) modulo powers of a prime

Cites Work

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• On exponential sums over multiplicative subgroups of medium size
• Sum-Products Estimates with Several Sets and Applications
• Congruences involving product of intervals and sets with small multiplicative doubling modulo a prime and applications
• On the number of solutions of exponential congruences
• On Residues of n n
• Some heuristics and results for small cycles of the discrete logarithm

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