• Corpus ID: 233241124

# Hilbert's Tenth Problem: Refinements and Variants

```@inproceedings{Gasarch2021HilbertsTP,
title={Hilbert's Tenth Problem: Refinements and Variants},
author={William I. Gasarch},
year={2021}
}```
Hilbert’s 10th problem, stated in modern terms, is Find an algorithm that will, given p ∈ Z [ x 1 , . . . , x n ] , determine if there exists a 1 , . . . , a n ∈ Z such that p ( a 1 , . . . , a n ) = 0 . Davis, Putnam, Robinson, and Matijaseviˇc showed that there is no such algorithm. We look at what happens (1) for ﬁxed degree and number of variables, (2) for particular equations, and (3) for variants which reduce the number of variables needed for undecidability results.
2 Citations
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