# 1. (4 points) The algorithm below purports to decide Hilbert’s 10th problem, finding integral ro

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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