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A Fermat-Like Sequence and Primes of the Form $2h.3^n+1$

Yannick Saouter 1
1 API - Parallel VLSI Architectures
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : Fermat numbers are a classical topic in elementary number theory. Fermat introduced them and claimed that all these numbers are prime. This claim was disproofed by Euler who gave a property on the eventual divisors of the Fermat numbers. In this article we exhibit another serie whose definition is close to the one of Fermat numbers and which exhibit similar properties. This problem will lead us to the sets of covering congruences for numbers $2h.3^n+1$ as similarly Fermat numbers lead to Sierpinski's problem.
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Submitted on : Wednesday, May 24, 2006 - 2:11:30 PM
Last modification on : Friday, February 4, 2022 - 3:12:27 AM
Long-term archiving on: : Monday, April 5, 2010 - 12:02:45 AM


  • HAL Id : inria-00073966, version 1


Yannick Saouter. A Fermat-Like Sequence and Primes of the Form $2h.3^n+1$. [Research Report] RR-2728, INRIA. 1995. ⟨inria-00073966⟩



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