1. (4 points) The algorithm below purports to decide Hilbert's 10th
problem, finding integral roots for polynomials with multiple variables
(that is, to decide the the Diophantine equations):
input: a polynomial p over k variables v1 … vk, where k > 1:
Repeat for all possible integral settings of v1… vk
if p = 0 for some combination of variable settings, accept.
Reject, because p ≠ 0 for all possible integral settings of v1 … vk.
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Do you think this is a valid decision procedure? If not, say specifically what the problems is.