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.

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Full text arXiv 2104.07220: pdf, ps.