Resumen de Values of the Euler Function in Various Sequences

William D. Banks, Kevin Ford, Florian Luca, Francesco Pappalardi, Igor E. Shparlinski

• Let ?(n) and ?(n) denote the Euler and Carmichael functions, respectively. In this paper, we investigate the equation ?(n)r = ?(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 ?(n) = p - 1 holds with some prime p, as well as those positive integers n such that the equation ?(n) = f(m) holds with some integer m, where f is a fixed polynomial with integer coefficients and degree degf > 1.