Undecidability on Diophantine equations over $\mathbb{Z}[i]$ with $20$ unknowns

Yuri Matiyasevich, Zhi-Wei Sun

It is known that Hilbert's Tenth Problem over the Gaussian ring $\mathbb{Z}[i]=\{a+bi:a,b\in \mathbb{Z}\}$ is undecidable. In this paper we obtain the following further result: Ther…