On Diophantine equations over $\mathbb Z[i]$ with $52$ unknowns

Yuri Matiyasevich; Zhi-Wei Sun

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On Diophantine equations over mathbb Z[i] with 52 unknowns

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arxiv 2002.12136 v3 pith:SAJN56YY submitted 2020-02-24 math.NT math.LO

On Diophantine equations over mathbb Z[i] with 52 unknowns

Yuri Matiyasevich , Zhi-Wei Sun This is my paper

classification math.NT math.LO

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In this paper we show that there is no algorithm to decide whether an arbitrarily given polynomial equation $P(z_1,\ldots,z_{52})=0$ (with integer coefficients) over the Gaussian ring $\mathbb Z[i]$ is solvable.

On Diophantine equations over mathbb Z[i] with 52 unknowns

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