L. H. Gallardo

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20232026

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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.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 =…

math.NT2023

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…