Hilbert's Tenth Problem

Hilbert's tenth problem is the tenth on the list of Hilbert's problems of 1900. Its statement is as follows:

Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in rational integers.

A Diophantine equation is an equation of the form

where p is a polynomial with integer coefficients. It took many years for the problem to be solved with a negative answer. Today, it is known that no such algorithm exists in the general case. This result is the combined work of Martin Davis, Yuri Matiyasevich, Hilary Putnam and Julia Robinson.

Read more about Hilbert's Tenth Problem:  Formulation, Diophantine Sets, History, Applications, Further Results, Extensions of Hilbert's Tenth Problem

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