Abstract

In a previous paper of the author it was shown that the question whether systems of exponential diophantine equations are solvable in $${\mathbb {Q}}$$ is undecidable. Now we show that the solvability of a conjunction of exponential diophantine equations in $${\mathbb {Q}}$$ is equivalent to the solvability of just one such equation. It follows that the problem whether an exponential diophantine equation has solutions in $${\mathbb {Q}}$$ is undecidable. We also show that two particular forms of exponential diophantine equations are undecidable.