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Journal of Applied Mathematics and Computation

The Investigation of Euler’s Totient Function Preimages

Author:Ruslan Skuratovskii Date:March 29,2019 Hits:

Abstract

We propose a lower bound for computing quantity of the inverses of Euler’s function. We answer the question about the multiplicity of m in the equation φ(x) = m [5]. An analytic expression for exact multiplicity of m = 22n + a, where a ∈ N , a < 2n, φ(t) = 22n + a was obtained. A lower bound of inverses number for arbitrary m was found. We make an approach to Sierpinski assertion from new side. New numerical metric was proposed.

References

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The Investigation of Euler’s Totient Function Preimages


Ruslan Skuratovskii

Kiev, MAUP, Faculty of Computer Sciences, Ukraine


*Corresponding author: Ruslan Skuratovskii, Kiev, MAUP, Faculty of Computer Sciences, Ukraine. 


Email: ruslan@unicyb.kiev.ua, ruslcomp@mail.ru


How to cite this paper:  Ruslan Skuratovskii. (2019) The Investigation of Euler’s Totient Function Preimages. J ournal o f Ap plied Mathematics and Computation, 3(3), 591-598. 


DOI: 10.26855/jamc.2019.03.001

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