WebOct 14, 2024 · So, my questions are: do there exist an algorithm to solve the Hilbert 10th problem for all genus $2$ equations? If not, are you aware of any examples for which the problem seems difficult? Are there such examples of degree 4? nt.number-theory; algebraic-number-theory; diophantine-equations; computational-number-theory; WebJul 14, 2024 · N.Garc\'ia-Fritz and H.Pasten showed that Hilbert's 10th problem is unsolvable in the ring of integers of number fields of the form $\mathbb{Q}(\sqrt[3]{p},\sqrt{-q})$ for positive proportions of ...
Diophantine Equation -- from Wolfram MathWorld
WebApr 11, 2024 · Hilbert 10th problem for cubic equations Asked 9 months ago Modified 4 months ago Viewed 263 times 6 Hilbert 10th problem, asking for algorithm for determining whether a polynomial Diopantine equation has an integer solution, is undecidable in general, but decidable or open in some restricted families. http://www.cs.ecu.edu/karl/6420/spr16/Notes/Reduction/hilbert10.html consolidated communications in maine
Hilbert
WebMar 24, 2024 · A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary Diophantine equation has a solution. Such an algorithm does exist for the solution of first-order Diophantine equations. WebJulia Robinson and Hilbert's. 10. th Problem. Julia Robinson and Martin Davis spent a large part of their lives trying to solve Hilbert's Tenth Problem: Does there exist an algorithm to determine whether a given Diophantine equation had a solution in rational integers? In fact no such algorithm exists as was shown by Yuri Matijasevic in 1970. WebHilbert spurred mathematicians to systematically investigate the general question: How solvable are such Diophantine equations? I will talk about this, and its relevance to speci c … consolidated communications mn