Number Theory

    

On the Prime Decomposition of Integers of the Form (Z^n-Y^n)/(z-y)

Authors: Rachid Marsli

In this work, the author shows a sufficient and necessary condition for an integer of the form (z^n-y^n)/(z-y) to be divisible by some perfect mth power p^m,where p is an odd prime and m is a positive integer. A constructive method of this type of integers is explained with details and examples. Links beetween the main result and known ideas such as Fermat’s last theorem, Goor-maghtigh conjecture and Mersenne numbers are discussed. Other relatedideas, examples and applications are provided.

Comments: 17 Pages.

Download: PDF

Submission history

[v1] 2019-01-01 16:19:56
[v2] 2019-06-04 05:20:45

Unique-IP document downloads: 268 times

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