JP Journal of Algebra, Number Theory and Applications
Volume 44, Issue 1, Pages 41 - 61
(October 2019) http://dx.doi.org/10.17654/NT044010041 |
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ON THE PRIME DECOMPOSITION OF INTEGERS OF THE FORM
Rachid Marsli
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Abstract: In this work, we obtain a necessary and sufficient condition for an integer of the form to be divisible by some perfect mth power 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 between the main result and known ideas such as Fermat’s last theorem, Goormaghtigh conjecture and Mersenne numbers are discussed. Other related ideas, examples and applications are provided. |
Keywords and phrases: primitive root modulo integer, prime, perfect nth power, Fermat’s last theorem, Goormaghtigh conjecture.
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