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November 2013 On Williams Numbers with Three Prime Factors
Ibrahim Al-Rasasi, Nejib Ghanmi
Missouri J. Math. Sci. 25(2): 134-152 (November 2013). DOI: 10.35834/mjms/1384266199

Abstract

Let $a\in \mathbb{Z}\setminus \{0\}$. A positive squarefree integer $N$ is said to be an $a$-Korselt number ($K_{a}$-number, for short) if $N\neq a$ and $p-a$ divides $N-a$ for each prime divisor $p$ of $N$. By an $a$-Williams number ($W_{a}$-number, for short) we mean a positive integer which is both an $a$-Korselt number and $(-a)$-Korselt number. This paper proves that for each $a$ there are only finitely many $W_{a}$-numbers with exactly three prime factors, as conjectured in 2010 by Bouallegue-Echi-Pinch.

Citation

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Ibrahim Al-Rasasi. Nejib Ghanmi. "On Williams Numbers with Three Prime Factors." Missouri J. Math. Sci. 25 (2) 134 - 152, November 2013. https://doi.org/10.35834/mjms/1384266199

Information

Published: November 2013
First available in Project Euclid: 12 November 2013

zbMATH: 1303.11016
MathSciNet: MR3161630
Digital Object Identifier: 10.35834/mjms/1384266199

Subjects:
Primary: 11Y16
Secondary: 11A51, 11Y11

Rights: Copyright © 2013 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.25 • No. 2 • November 2013
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