Page "Hilbert's tenth problem" Paragraph 12

Conversely, an algorithm to test for solvability in arbitrary integers could be used to test a given equation for solvability in natural numbers by applying that supposed algorithm to the equation obtained from the given equation by replacing each unknown by the sum of the squares of four new unknowns.

This works because of Lagrange's four-square theorem, to the effect that every natural number can be written as the sum of four squares.