Missouri Journal of Mathematical Sciences

On Williams Numbers with Three Prime Factors

Ibrahim Al-Rasasi and Nejib Ghanmi

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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.

Article information

Missouri J. Math. Sci., Volume 25, Issue 2 (2013), 134-152.

First available in Project Euclid: 12 November 2013

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11Y16: Algorithms; complexity [See also 68Q25]
Secondary: 11Y11: Primality 11A51: Factorization; primality

Carmichael number Korselt number Williams number Prime number squarefree composite number


Al-Rasasi, Ibrahim; Ghanmi, Nejib. On Williams Numbers with Three Prime Factors. Missouri J. Math. Sci. 25 (2013), no. 2, 134--152. doi:10.35834/mjms/1384266199. https://projecteuclid.org/euclid.mjms/1384266199

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