Institute of Mathematics Conferences, Sixth International Conference on Analytic Number Theory and Spatial Tessellations

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The investigation of Euler's totient function preimages
Ruslan Skuratovskii, Dmitriy Rudenko

Building: Mykhailo Drahomanov National Pedagogical University
Room: Room A
Date: 2018-09-28 05:05 PM – 17:35
Last modified: 2018-09-24


Using the properties of the Euler's function, we found a way of calculating the number of preimages from large powers of two.  Also it was found a way to establish the exact number of preimages for a number of the form ${{2}^{{{2}^{n}}+a}},\,\,\,a<{{2}^{n}}$.  If the number ${{2}^{{{2}^{n}}+1}}$ is not prime. In the case if ${{2}^{{{2}^{n}}+1}}$ is  a simple one, a lower bound is found for the number of preimages of such a number.