Congruences and Rational Exponential Sums with the Euler Function

William D. Banks, Igor E. Shparlinski

Type: Article

Publication Date: 2006-10-01

Citations: 8

DOI: https://doi.org/10.1216/rmjm/1181069373

Abstract

We give upper bounds for the number of solutions to congruences with the Euler function ϕ(n) modulo an integer q ≥ 2. We also give nontrivial bounds for rational exponential sums with ϕ(n)/q.

Locations

Rocky Mountain Journal of Mathematics - View - PDF

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+	On the Normal Behavior of the Iterates Of some Arithmetic Functions	1990	Paul Erdős Andew Granvilie Carl Pomerance Claudia Spiro
+	Introduction to Analytic and Probabilistic Number Theory	2015	Gérald Tenenbaum
+	Mean Value Theorems in Prime Number Theory	1975	R. C. Vaughan
+	On the number of prime factors of an integer	1988	Adolf Hildebrand Gérald Tenenbaum
+ PDF Chat	Integers without large prime factors	1993	Adolf Hildebrand Gérald Tenenbaum
+	On a problem of Oppenheim concerning “factorisatio numerorum”	1983	E. Rodney Canfield Paul Erdős Carl Pomerance
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+ PDF Chat	On some problems of Mąkowski–Schinzel and Erdős concerning the arithmetical functions φ and σ	2002	Florian Luca Carl Pomerance
+	On the prime power divisors of the iterates of the Euler-$\phi$ function	1999	N. L. Bassily I. Kátai M. Wijsmuller