L. Gallardo

activity

20072023

F_{2}

with four prime factors

8 citations · 12 across the 17 of their papers we have counts for

collaborators

18 papers

math.NT2023

On splitting bi-unitary perfect polynomials over $F_{p^{2}}$

Luis H. Gallardo, Olivier Rahavandrainy

We give all splitting bi-unitary perfect polynomials over the field $F_{4}$ and some splitting ones over $F_{p^{2}}$ , if $p$ is an odd prime.

math.NT2023

On Collatz Conjecture for binary polynomials

Luis H. Gallardo, Olivier Rahavandrainy

We build a variant of Collatz Conjecture for polynomials over $F_{2}$ and we prove that it is solved. By the way, we give several examples.

math.NT2023

On odd perfect numbers of special forms

Luis H. Gallardo, Olivier. Rahavandrainy

We give necessary conditions for perfection of some families of odd numbers with special multiplicative forms. Extending earlier work of Steuerwald, Kanold, McDaniel et al.

math.NT2023

Fixed points of the sum of divisors function on $F_{2} [x]$

Luis H. Gallardo

We work an analogue of a classical arithmetic problem over polynomials. More precisely, we study the fixed points $F$ of the sum of divisors function $σ : F_{2} [x] \mapsto F_{2} [x]$ (de…

math.NT2023

Some multiplicative functions over $F_{2}$

Luis H. Gallardo, Olivier Rahavandrainy

We adapt (over $F_{2}$ ) the general notions of multiplicative function, Dirichlet convolution and Inverse. We get some interesting results, namely necessary conditions for a…

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…

On splitting bi-unitary perfect polynomials over Fp2​

On Collatz Conjecture for binary polynomials

On odd perfect numbers of special forms

Fixed points of the sum of divisors function on F2​[x]

Some multiplicative functions over F2​

All bi-unitary perfect polynomials over $\F_2$ with only Mersenne primes as odd divisors

On splitting bi-unitary perfect polynomials over $F_{p^{2}}$

Fixed points of the sum of divisors function on $F_{2} [x]$

Some multiplicative functions over $F_{2}$