Diophantine equation
Number theory
A polynomial equation, or system of equations, with integer coefficients, for which integer solutions are sought.
What is usually left out
Restricting to integers changes the problem completely: x² + y² = z² has a continuum of real solutions and a rich but discrete set of integer ones. Hilbert’s tenth problem asked for a general algorithm deciding whether such an equation has an integer solution; Matiyasevich completed a proof in 1970 that no such algorithm exists.