  Let $K$ be a field of characteristic zero and $k$ and $l$ be two
multiplicatively independent positive integers. We prove the following result
that was conjectured by Loxton and van der Poorten during the Eighties: a power
series $F(z)\in K[[z]]$ satisfies both a $k$- and a $l$-Mahler type functional
equation if and only if it is a rational function.
