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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

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classification math.NT math.LO
keywords mathbbalgorithmarbitrarilycoefficientsdecidediophantineequationequations
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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.

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