Polynomial Extensions of a Putnam Delight

摘要

Fibonacci, Lucas, Pell, and Pell-Lucas polynomials are a fertile ground for imagination and creativity. They offer boundless exploratory opportunities for Fibonacci and Lucas enthusiasts. This article features one such activity; it extends a Fibonacci problem that appeared in the 68th William Putnam Mathematical Competition to Fibonacci, Lucas, Pell, and Pell-Lucas polynomials.