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math.NT2025
A variant of Collatz's Conjecture over Binary Polynomials
Luis H. Gallardo, Olivier Rahavandrainy
We study a natural analogue of Collatz's Conjecture for polynomials over .
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.NT2019
A Real eigenvector of Circulant matrices and a conjecture of Ryser
Luis H. Gallardo
We prove that there is no circulant Hadamard matrix with first row of order , under a condition about a sum of scalar products of rows of two other…