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-…