L. H. Gallardo

activity

20242026

collaborators

6 papers

math.NT2026

Splitting sums of binary polynomials

Luis H. Gallardo

We study an analogue of a classical arithmetic problem over the ring of polynomials. We prove that $m = 5$ is the minimal number such that the sums of any two distinct polynomials…

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 $F_{2}$ .

math.NT2025

On Ryser's Conjecture

Antun Domic, Luis H. Gallardo

We provide new sufficient conditions under which Ryser's conjecture holds.

math.NT2025

A Note on a Result of Makowski

Luis H. Gallardo, Joshua Zelinsky

In this note, we fix a gap in a proof of the first author that 28 is the only even perfect number which is the sum of two perfect cubes. We also discuss the situation for higher po…

math.CO2024

Combinatorial properties of Circulant Hadamard matrices

Luis H. Gallardo, Olivier Rahavandrainy, Reinhardt. Euler

We describe combinatorial properties of the defining row of a circulant Hadamard matrix by exploiting its orthogonality to subsequent rows, and show how to exclude several particul…

math.NT2024

Ryser's Conjecture and Stochastic matrices

Luis H. Gallardo

Assume that $H$ is a circulant Hadamard matrix of order $n \geq 4$ . We consider an appropriate stochastic matrix $S$ of order $n$ depending on $H$ . This allows us to prove that $n =…