Steven J. Miller

activity

20232026

collaborators

12 papers

math.HO2026

Why Does the Slope Definition of $e$ Work?: A Self-Contained Exploration After Real Analysis

Hung Viet Chu, Steven J. Miller, Joshua M. Siktar

Euler's number $e$ is often introduced through compound interest, an infinite series, an area, or the slope of an exponential function. The last viewpoint is especially attractive:…

math.NT2026

Generalizing a Pair of Diophantine Equations

Hung Viet Chu, Dongho Kim, Theodore Koch +2

For coprime integers $a$ and $b$ , it is known that exactly one of the two Diophantine equations $$ ax+by\ =\ \frac{(a-1)(b-1)}{2} \qquad\text{and}\qquad 1+ax+by\ =\ \frac{(a-1)(b-1…

math.CO2026

Counting Schreier Sets Under Neighborhood Conditions

Ben Chen, Hung Viet Chu, Corbin F. Foss +4

We count Schreier sets that satisfy a neighborhood condition, including $k$ -clustered, $k$ -consecutive-free, $k$ -neighbored, $k$ -isolated, and closed under integral $2$ -averages. F…

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.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…

math.HO2024

Composite Numbers in an Arithmetic Progression

Hung Viet Chu, Steven J. Miller, Joshua M. Siktar

One challenge (or opportunity!) that many instructors face is how varied the backgrounds, abilities, and interests of students are. In order to simultaneously instill confidence in…

math.NT2024

A Pair of Diophantine Equations Involving the Fibonacci Numbers

Xuyuan Chen, Hung Viet Chu, Fadhlannafis K. Kesumajana +5

Let $a, b \in N$ be relatively prime. Previous work showed that exactly one of the two equations $a x + b y = (a - 1) (b - 1) /2$ and $a x + b y + 1 = (a - 1) (b - 1) /2$ has a nonnegative…

math.NT2024

Sum of Consecutive Terms of Pell and Related Sequences

Navvye Anand, Amit Kumar Basistha, Kenny B. Davenport +4

We study new identities related to the sums of adjacent terms in the Pell sequence, defined by $P_{n} := 2 P_{n - 1} + P_{n - 2}$ for $n \geq 2$ and $P_{0} = 0, P_{1} = 1$ , and generalize the…

math.NT2023

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…

Why Does the Slope Definition of e Work?: A Self-Contained Exploration After Real Analysis