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.
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
SN - 0026-9255
VL - 146
SP - 1
EP - 19
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
IS - 1
ER -