Steven J. Miller

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20232026

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math.NT2025

Problems Regarding a Pair of Diophantine Equations

Hung Viet Chu, Steven J. Miller, Garrett Tresch

For two relatively prime positive integers $a, b \in N$ , it is known that exactly one of the two Diophantine equations $$ax + by \ =\ \frac{(a-1)(b-1)}{2}\ \mbox{ and }\ 1…

math.PR2025

On a Roll Again: Analysis of a Dice Removal Game

Francesco Camellini, Wissam Ghantous, Andrea M. Lanocita +4

Suppose we have $n$ dice, each with $s$ faces (assume $s \geq n$ ). On the first turn, roll all of them, and remove from play those that rolled an $n$ . Roll all of the remaining dice…

math.NT2025

A Pair of Diophantine Equations and Fibonacci-Like Sequences

Hung Viet Chu, Rishabh Gulecha, Sicheng Guo +3

Given two relatively prime numbers $a$ and $b$ , it is known that exactly one of the two Diophantine equations has a nonnegative integral solution $(x, y)$ : $$ ax + by \ =\ \frac{(a-…

math.CO2025

Linear Recurrences from Counting Schreier-Type Multisets

Hung Viet Chu, Yubo Geng, Julian King +3

A nonempty set $F$ is Schreier if $min F \geq ∣ F ∣$ . Bird observed that counting Schreier sets in a certain way produces the Fibonacci sequence. Since then, various connections betwe…