Schinzel's theorem

Schinzel's theorem is a result in number theory related to prime numbers and algebraic expressions. Specifically, it concerns the values of certain polynomial expressions and their ability to yield prime numbers for infinitely many integers. The theorem states that if \(P(x)\) is a polynomial with integer coefficients that takes on prime values for infinitely many integers \(x\), then it can be combined with another polynomial \(Q(x)\) to form a new polynomial that also takes prime values for infinitely many integers.