Study of Korselt Numbers and Sets between Theory and Application

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Eshtaya, Abeer Adel Mohammad
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جامعة النجاح الوطنية
The Korselt numbers and sets were discussed for the first time in 2007. The problem can be considered as a new one with limited literature making it as a new field of research. Let N be a positive integer and α a non-zero integer. If N 6= α and p − α divides N − α for each prime divisor p of N, then N is called an α-Korselt number (Kα-number). The set of all α such that N is a Kα-number is called the Korselt set of N. The concept of Kα-number was introduced by Othman Echi in 2007 and recently studied for different situation of N by Othman Echi, Nejib Ghanmi, Kais Bouallgu and Richard Pinch. Here it should be noted that the concept of Korselt numbers generalizes another concept called the Carmichael numbers which was presented as a counterexam ple for the converse of Fermat’s little theorem. This Thesis contributes to study, validate and develop all results mentioned in the papers. Also it contributes to use the developed results to build algorithms by MATLAB that will enrich the literature with Korselt sets of relatively large numbers (not included in the literature) as well as testing and illustrating the involved theory