Schinzel's hypothesis H

English

Etymology

Named after Andrzej Schinzel.

Proper noun

Schinzel's hypothesis H

1. (number theory) A famous open problem in mathematics, the hypothesis stating that, for every finite collection $\{f_{1},f_{2},\ldots ,f_{k}\}$ 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 $f_{1}(n),f_{2}(n),\ldots ,f_{k}(n)$ are simultaneously prime numbers, or (ii) there is an integer $m>1$ (called a fixed divisor) which always divides the product $f_{1}(n)f_{2}(n)\cdots f_{k}(n)$.