On $k$-th power Diophantine triples of the form $\{a^k,b,c\}$

Clemens Fuchs, Miriam Schönauer

In this paper, we prove that there are no $k$-th power Diophantine triples of the form $\{a^k,b,c\}$ for $k\ge 3$ and $1<a^k<b<c$.