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math.NT2022
All bi-unitary perfect polynomials over $\F_2$ with only Mersenne primes as odd divisors
Luis H. Gallardo, Olivier Rahavandrainy
The paper is about a polynomial variant of a classical arithmetic problem. More precisely, we obtain all non-splitting bi-unitary perfect polynomials over the prime field of two el…
math.NT2022
Admissible family for binary perfect polynomials
Luis H. Gallardo, Olivier Rahavandrainy
The paper is about an arithmetic problem in $\F_2[x]$. We give \emph{admissible} (necessary) conditions satisfied by a set of odd prime divisors of perfect polynomials over $\F_2$.…
math.NT2022
All even (unitary) perfect polynomials over $\F_2$ with only Mersenne primes as odd divisors
Luis H. Gallardo, Olivier Rahavandrainy
We address an arithmetic problem in the ring $\F_2[x]$ related to the fixed points of the sum of divisors function. We study some binary polynomials such that is stil…