Skolem's theorem

Skolem's theorem is a result in mathematical logic and number theory that concerns solutions to certain types of equations called polynomial equations. It states that if a polynomial equation with integer coefficients has a solution in some larger algebraic setting (like fractions or complex numbers), then it must also have solutions within a more "regular" domain called the integers or algebraic integers, depending on context. In simple terms, the theorem guarantees that, for specific equations, solutions aren't just found in complicated or extended number systems but can also be found within more familiar ones, ensuring a certain kind of consistency in solutions.