On (unitary) perfect polynomials over F2 with only Mersenne primes as odd divisors
Luis H. Gallardo, Olivier Rahavandrainy · HAL (Le Centre pour la Communication Scientifique Directe) · 2024
The only (unitary) perfect polynomials over F2 with only Mersenne primes as odd divisors that are products of $x$, $x+1$ and 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 $h$. Other consequences of such a factorization are new results about odd perfect polynomials.