Steven J. Miller

collaborators

7 papers

math.NT2026

On Zeckendorf-Niven numbers and arithmetic progressions

Kelly Lao, Steven J. Miller, Nicholas Rosa +4

A positive integer is Zeckendorf-Niven (respectively, Lucas-Niven) if it is divisible by the number of summands in its Zeckendorf decomposition (respectively, Lucas decomposition).…

math.PR2026

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.NT2026

On a Pair of Diophantine Equations

Sujith Uthsara Kalansuriya Arachchi, Hung Viet Chu, Jiasen Liu +3

For relatively prime natural numbers $a$ and $b$ , we study the two equations $a x + b y = (a - 1) (b - 1) /2$ and $a x + b y + 1 = (a - 1) (b - 1) /2$ , which arise from the study of cyclotomic polynomial…

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.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…