Steven J. Miller

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20232026

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3 papers · 1 filter

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…