**Hilbert’s tenth problem concerns **finding an algorithm to determine whether a given polynomial Diophantine equation with integer coefficients has an integer solution.

Polynomial equations in a finite number of variables with integer coefficients are known as Diophantine equations. Equations like *x ^{2} − y^{3} = 7* and

*x*are examples. For centuries, mathematicians have wondered whether certain Diophantine equations have integer solutions. Hilbert’s 10th problem asks whether there is an algorithm to determine whether a given Diophantine equation has integer solutions or not. In 1970, Yuri Matiyasevich completed a proof that no such algorithm exists.

^{2}+ y^{2}= z^{2}