Conjunctions of exponential diophantine equations over \({\mathbb {Q}}\)

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.