Schinzel's hypothesis H

English

Named after Template:W.

Template:Lb A famous open problem in mathematics, the hypothesis stating that, for every finite collection ${f_{1}, f_{2}, \dots, f_{k}}$ of non-constant irreducible polynomials over the integers with positive leading coefficients, one of the following conditions holds: (i) there are infinitely many positive integers $n$ such that all of $f_{1} (n), f_{2} (n), \dots, f_{k} (n)$ are simultaneously prime numbers, or (ii) there is an integer $m > 1$ (called a fixed divisor) which always divides the product $f_{1} (n) f_{2} (n) \dots f_{k} (n)$ .