ALL EVEN (UNITARY) PERFECT POLYNOMIALS OVER F 2 WITH ONLY MERSENNE PRIMES AS ODD DIVISORS - Université de Bretagne Occidentale Access content directly
Journal Articles Kragujevac Journal of Mathematics Year : 2022

ALL EVEN (UNITARY) PERFECT POLYNOMIALS OVER F 2 WITH ONLY MERSENNE PRIMES AS ODD DIVISORS

Abstract

We address an arithmetic problem in the ring F 2 [x]. We prove that the only (unitary) perfect polynomials over F 2 that are products of x, x + 1 and of Mersenne primes are precisely the nine (resp. nine "classes") known ones. This follows from a new result about the factorization of M 2h+1 + 1, for a Mersenne prime M and for a positive integer h.
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Dates and versions

hal-04344292 , version 1 (14-12-2023)

Identifiers

  • HAL Id : hal-04344292 , version 1

Cite

Luis H Gallardo, Olivier Rahavandrainy. ALL EVEN (UNITARY) PERFECT POLYNOMIALS OVER F 2 WITH ONLY MERSENNE PRIMES AS ODD DIVISORS. Kragujevac Journal of Mathematics, 2022. ⟨hal-04344292⟩

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