Fibonacci Numbers and Vieta Jumping for a Rational Diophantine Equation

Steven J. Miller, Dimitrios Nikolakopoulos, Anitha Srinivasan

We study the Diophantine equation $\frac{a+1}{b}+\frac{b+1}{a}=k$, where $k$ is an integer. Using Vieta jumping, we completely classify all positive intege…