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A NOTE ON GENERALISED WALL–SUN–SUN PRIMES
Published online by Cambridge University Press: 28 February 2023
Abstract
Let a and b be positive integers and let $\{U_n\}_{n\ge 0}$ be the Lucas sequence of the first kind defined by
We define an $(a,b)$-Wall–Sun–Sun prime to be a prime p such that $\gcd (p,b)=1$ and $\pi (p^2)=\pi (p),$ where $\pi (p):=\pi _{(a,b)}(p)$ is the length of the period of $\{U_n\}_{n\ge 0}$ modulo p. When $(a,b)=(1,1)$, such primes are known in the literature simply as Wall–Sun–Sun primes. In this note, we provide necessary and sufficient conditions such that a prime p dividing $a^2+4b$ is an $(a,b)$-Wall–Sun–Sun prime.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 108 , Issue 3 , December 2023 , pp. 373 - 378
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
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