TY - JOUR

T1 - Values of the Euler function in various sequences

AU - Banks, William D.

AU - Ford, Kevin

AU - Luca, Florian

AU - Pappalardi, Francesco

AU - Shparlinski, Igor E.

N1 - Copyright:
Copyright 2005 Elsevier B.V., All rights reserved.

PY - 2005/9

Y1 - 2005/9

N2 - Let φ(n) and λ(n) denote the Euler and Carmichael functions, respectively. In this paper, we investigate the equation φ(n) r = λ(n) s , where r ≥ s ≥ 1 are fixed positive integers. We also study those positive integers n, not equal to a prime or twice a prime, such that φ(n) = p - 1 holds with some prime p, as well as those positive integers n such that the equation φ(n) = f(m) holds with some integer m, where f is a fixed polynomial with integer coefficients and degree degf > 1.

AB - Let φ(n) and λ(n) denote the Euler and Carmichael functions, respectively. In this paper, we investigate the equation φ(n) r = λ(n) s , where r ≥ s ≥ 1 are fixed positive integers. We also study those positive integers n, not equal to a prime or twice a prime, such that φ(n) = p - 1 holds with some prime p, as well as those positive integers n such that the equation φ(n) = f(m) holds with some integer m, where f is a fixed polynomial with integer coefficients and degree degf > 1.

KW - Carmichael function

KW - Euler function

KW - Polynomials

KW - Primes

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U2 - 10.1007/s00605-005-0302-7

DO - 10.1007/s00605-005-0302-7

M3 - Article

AN - SCOPUS:24344478728

VL - 146

SP - 1

EP - 19

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 1

ER -