
TL;DR
This paper investigates Korselt bases for positive integers, proving finiteness of the set of rational Korselt bases for squarefree composite numbers and establishing bounds and conditions for these bases.
Contribution
It introduces the concept of Korselt bases in rational numbers and proves the finiteness of these sets for squarefree composite numbers, providing bounds and conditions.
Findings
The set of rational Korselt bases for squarefree composite numbers is finite.
Bounds for Korselt bases in rational numbers are established.
Necessary and sufficient conditions for the bounds to be reached are provided.
Abstract
For a positive integer and a subset of , let - denote the set of verifying divides for every prime divisor of . The set - is called the set of Korselt bases of in or simply the -Korselt set of . In this paper, we prove that for each squarefree composite number the -Korselt set of is finite where we provide an upper and lower bounds for each Korselt base of in . Furthermore, we give a necessary and a sufficient condition for the upper bound of a Korselt base to be reached.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Finite Group Theory Research
