The investigation of Euler's totient function preimages

Publication date: 30 November 2018

Abstract: We propose a lower estimation for computing quantity of the inverses of Euler's function. We answer the question about the multiplicity of

m

in the equation

v a r p h i (x) = m

cite{Ford}. An analytic expression for exact multiplicity of

m = 2^{2^{n} + a}

, where

a i n N

,

a < 2^{n}

,

v a r p h i (t) = 2^{2^{n} + a}

was obtained. A lower bound of inverses number for arbitrary

m

was found. New numerical metric was proposed.

Mathematics Subject Classification ID

Other abelian and metabelian extensions (11R20)

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