6 papers
Schreier-Type Sets and Linear Recurrences: Connections and Developments
Hung Viet Chu
We demonstrate several common techniques for proving linear recurrences from counting Schreier-type sets. These techniques include formula-based arguments, bijective proofs, mathem…
On a Pair of Diophantine Equations
Sujith Uthsara Kalansuriya Arachchi, Hung Viet Chu, Jiasen Liu +3
For relatively prime natural numbers and , we study the two equations and , which arise from the study of cyclotomic polynomial…
Problems Regarding a Pair of Diophantine Equations
Hung Viet Chu, Steven J. Miller, Garrett Tresch
For two relatively prime positive integers , it is known that exactly one of the two Diophantine equations $$ax + by \ =\ \frac{(a-1)(b-1)}{2}\ \mbox{ and }\ 1…
A Pair of Diophantine Equations and Fibonacci-Like Sequences
Hung Viet Chu, Rishabh Gulecha, Sicheng Guo +3
Given two relatively prime numbers and , it is known that exactly one of the two Diophantine equations has a nonnegative integral solution : $$ ax + by \ =\ \frac{(a-…
Linear Recurrences from Counting Schreier-Type Multisets
Hung Viet Chu, Yubo Geng, Julian King +3
A nonempty set is Schreier if . Bird observed that counting Schreier sets in a certain way produces the Fibonacci sequence. Since then, various connections betwe…
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…