4 papers
Gaps for PLRS with zero coefficients
Yinxi Chen, Zongyun Chen, Brian Hii +1
Zeckendorf proved that every positive integer has a unique decomposition as a sum of non-adjacent Fibonacci numbers. Among its extensions, we focus on Positive Linear Recurrence Se…
Fibonacci Numbers and Vieta Jumping for a Rational Diophantine Equation
Steven J. Miller, Dimitrios Nikolakopoulos, Anitha Srinivasan
We study the Diophantine equation , where is an integer. Using Vieta jumping, we completely classify all positive intege…
Egg Drop Problems: They Are All They Are Cracked Up To Be!
Xiangwen Cao, Zongyun Chen, Steven J. Miller
We illustrate how to invite and excite students about research by exploring higher-dimensional generalizations of the classical egg drop problem, in which the goal is to locate a c…
Geometric Proof of the Irrationality of Square-Roots for Select Integers
Zongyun Chen, Steven J. Miller, Chenghan Wu
This paper presents geometric proofs for the irrationality of square roots of select integers, extending classical approaches. Building on known geometric methods for proving the i…