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June 9

Hilbert's tenth problem

Hilbert's tenth problem asked for a finite algorithm to decide whether a Diophantine equation has a solution. By 1970 it was proven that no such algorithm exists. The section Hilbert's tenth problem#Further results says Zhi Wei Sun showed that the problem for integers is unsolvable even for equations with no more than 11 unknowns.

1. Is there a value n such that an algorithm is known for deciding the existence of solutions for problems with no more than n unknowns?

2. If algorithms are known for problems with 2, or 3, unknowns, how do they work? Loraof (talk) 20:31, 9 June 2017 (UTC)[reply]

For n = 1, there is the rational root theorem. --JBL (talk) 02:15, 14 June 2017 (UTC)[reply]