• Corpus ID: 233241124

Hilbert's Tenth Problem: Refinements and Variants

  title={Hilbert's Tenth Problem: Refinements and Variants},
  author={William I. Gasarch},
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. 
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