The Korselt set of the square of a prime

Ibrahim Alrasasi

doi:10.1142/S1793042114500043

The Korselt set of the square of a prime

Ibrahim Alrasasi^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let α ∈ ℤ\{0}. A composite number N is said to be an α-Korselt number (K_α-number, for short) if N ≠ α and p - α divides N - α for each prime divisor p of N. The set of all α ∈ ℤ\{0} such that N is a K_α-number is called the Korselt set of N and is denoted by KS(N). In this paper, we study the Korselt set of q², where q is prime. We describe in detail how to obtain KS(q²), compute the cardinality of KS(q²), and answer some questions related to KS(q²).

Original language	English
Pages (from-to)	875-884
Number of pages	10
Journal	International Journal of Number Theory
Volume	10
Issue number	4
DOIs	https://doi.org/10.1142/S1793042114500043
State	Published - Jun 2014

Keywords

Carmichael number
Korselt number
Korselt set
Prime number
Square of a prime

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S1793042114500043

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N2 - Let α ∈ ℤ\{0}. A composite number N is said to be an α-Korselt number (Kα-number, for short) if N ≠ α and p - α divides N - α for each prime divisor p of N. The set of all α ∈ ℤ\{0} such that N is a Kα-number is called the Korselt set of N and is denoted by KS(N). In this paper, we study the Korselt set of q2, where q is prime. We describe in detail how to obtain KS(q2), compute the cardinality of KS(q2), and answer some questions related to KS(q2).

AB - Let α ∈ ℤ\{0}. A composite number N is said to be an α-Korselt number (Kα-number, for short) if N ≠ α and p - α divides N - α for each prime divisor p of N. The set of all α ∈ ℤ\{0} such that N is a Kα-number is called the Korselt set of N and is denoted by KS(N). In this paper, we study the Korselt set of q2, where q is prime. We describe in detail how to obtain KS(q2), compute the cardinality of KS(q2), and answer some questions related to KS(q2).

KW - Carmichael number

KW - Korselt number

KW - Korselt set

KW - Prime number

KW - Square of a prime

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EP - 884

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 4

ER -

The Korselt set of the square of a prime

Abstract

Keywords

ASJC Scopus subject areas

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