Joshua Zelinsky

activity

20242026

collaborators

9 papers

math.GM2026

On odd perfect numbers with exactly one even exponent greater than 2

Pascal Ochem, Joshua Zelinsky

We show that if all the even exponents of an odd perfect number N are equal to 2 except for one, then $3^{23, 000, 000, 000}$ divides N .

math.NT2026

Must a primitive non-deficient number have a component not much larger than its radical?

Joshua Zelinsky

Let $n$ be a primitive non-deficient number where $n = p_{1}^{a_{1}} p_{2}^{a_{2}} \dots p_{k}^{a_{k}}$ where $p_{1}, p_{2}, \dots, p_{k}$ are distinct primes. We prove that there exists an $i$ such…

math.NT2026

Complete characterization of $2$ -near perfect numbers with exactly 2 prime factors

Richard Fearon, Henry Foushee, Benjamin Porosoff +3

Let $I ¨ (n)$ be the sum of the positive divisors of $n$ . A positive integer $n$ is said to be $2$ -near perfect when $I ¨ (n) = 2 n + d_{1} + d_{2}$ , where $d_{1}$ and $d_{2}$ are distinct positive d…

math.CO2025

Dots and Boxes on Certain Families of Graphs

Vedant Aryan, Alana Palmer, Alexander Skula +2

We investigate the Dots and Boxes game, also known as ``Strings and Coins,'' for certain specific families of graphs. These include complete graphs, wheel graphs, and friendship gr…

math.NT2025

On near superperfect numbers, the Goormaghtigh conjecture, and Mertens' theorem

Satvik Beri, Joshua Zelinsky

Let $I ¨ (n)$ be the sum of the divisors of $n$ . Kalita and Saikia defined a number $n$ to be near superperfect if $2 n + d = I ¨ (I ¨ (n))$ for some positive divisor $d$ of $n$ . We extend so…

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…