A Pair of Diophantine Equations Involving the Fibonacci Numbers

Xuyuan Chen, Hung Viet Chu, Fadhlannafis K. Kesumajana +5

Let $a,b\in \mathbb{N}$ be relatively prime. Previous work showed that exactly one of the two equations $ax+by=(a-1)(b-1)/2$ and $ax+by+1=(a-1)(b-1)/2$ has a nonnegative…