Steven J. Miller

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20242026

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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.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.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…