J. A. Dris

activity

20112022

most citedOn a Curious Biconditional Involving Divisors of Odd Perfect Numbers

9 citations · 22 across the 16 of their papers we have counts for

collaborators

22 papers

math.NT2022

A new approach to odd perfect numbers via GCDs

Jose Arnaldo Bebita Dris

Let $q^{k} n^{2}$ be an odd perfect number with special prime $q$ . Define the GCDs $G = g cd (σ (q^{k}), σ (n^{2}))$ $H = g cd (n^{2}, σ (n^{2}))$ and $$I = \gcd\bigg(n,σ(n^2)…

math.GM2021

On the quantity $I (q^{k}) + I (n^{2})$ where $q^{k} n^{2}$ is an odd perfect number -- Part II

Keneth Adrian Precillas Dagal, Jose Arnaldo Bebita Dris

In this note, we continue an approach pursued in an earlier paper of the second author and thereby attempt to produce an improved lower bound for the sum $I (q^{k}) + I (n^{2})$ , where $…

math.NT2021

On the quantity $m^{2} - p^{k}$ where $p^{k} m^{2}$ is an odd perfect number -- Part II

Jose Arnaldo Bebita Dris, Immanuel Tobias San Diego

Let $p^{k} m^{2}$ be an odd perfect number with special prime $p$ . Extending previous work of the authors, we prove that the inequality $m < p^{k}$ follows from $m^{2} - p^{k} = 2^{r} t$ , wher…

math.NT2020★ 2 cited

Some Modular Considerations Regarding Odd Perfect Numbers

Jose Arnaldo Bebita Dris, Immanuel Tobias San Diego

Let $p^{k} m^{2}$ be an odd perfect number with special prime $p$ . In this article, we provide an alternative proof for the biconditional that $σ (m^{2}) \equiv 1 (mod 4)$ holds if and on…

math.NT2020

On the Existence of Odd Perfect Numbers

Jose Arnaldo Bebita Dris

In this paper, we prove the conjecture that if there is an odd perfect number, then there are infinitely many of them.

math.NT2017

Analysis of the Ratio $D (n) / n$

Jose Arnaldo B. Dris

In this note, we investigate properties of the ratio $D (n) / n$ , which we will call the deficiency index. We will discuss some concepts recast in the language of the deficiency index…