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Preprint Number 1967
1967. William Gasarch Hilbert's Tenth Problem: Refinements and Variants E-mail: Submission date: 15 April 2021 Abstract: Hilbert's 10th problem, stated in modern terms, is: Find an algorithm that will, given p in ℤ[x_1,...,x_n] determine if there exists a_1, a_2, ..., a_n in ℤ such that p(a_1,...,a_n)=0. Davis, Putnam, Robinson, and Matijasevic 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. Mathematics Subject Classification: Keywords and phrases: |

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