Abstract.
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.
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Banks, W., Ford, K., Luca, F. et al. Values of the Euler Function in Various Sequences. Mh Math 146, 1–19 (2005). https://doi.org/10.1007/s00605-005-0302-7
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DOI: https://doi.org/10.1007/s00605-005-0302-7