Conjunctions of exponential diophantine equations over ${\mathbb {Q}}$

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发表日期：

2025年1月3日

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Mihai Prunescu

摘要

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

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

摘要