Diophantine triples with values in $k$-generalized Fibonacci sequences

Clemens Fuchs, Christoph Hutle, Florian Luca +1

We show that if $k\ge 2$ is an integer and $(F_n^{(k)}{)}_{n\ge 0}$ is the sequence of $k$-generalized Fibonacci numbers, then there are only finitely many triples of positive intege…