Wikipedia:Reference desk/Archives/Mathematics/2017 June 9

= 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 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)


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