Hilbert's tenth problem

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Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm that, for any given Diophantine equation (a polynomial equation with integer coefficients and a finite number of unknowns), can decide whether the equation has a solution with all unknowns taking integer values. For example, the Diophantine equation 3 x 2 − 2 x y − y 2 z − 7 = 0 {\displaystyle 3x^{2}-2xy-y^{2}z-7=0} has an integer solution: x = 1 , y = 2 , z = − 2 {\displaystyle x=1,\ y=2,\ z=-2} . By contrast, the...

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