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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Mathematics [math]Origin | Files produced by the author(s) |
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