English Dictionary

Schinzel's hypothesis H

固有名詞

(number theory) A famous open problem in mathematics, the hypothesis stating that, for every finite collection f_1,f_2,…,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),…,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)⋯f_k(n).

日本語の意味

数論における著名な未解決問題であり、正の先行係数を持つ非定数の既約多項式 f₁, f₂, …, fₖ の有限集合について、(i) それらの全多項式の値が同時に素数となる正の整数 n が無限に存在するか、または (ii) その積 f₁(n)・f₂(n)・…・fₖ(n) に常に割り切れる 1 より大きい固定の整数（固定因子）が存在するかのいずれかが成立するという仮説

Many researchers still test Schinzel's hypothesis H by numerically searching for integers n that make several irreducible polynomials simultaneously prime.

多くの研究者は、複数の既約多項式が同時に素数になるような整数nを数値的に探索することで、シンツェルの仮説Hをいまだに検証している。

意味（1）

(number theory) A famous open problem in mathematics, the hypothesis stating that, for every finite collection f_1,f_2,…,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),…,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)⋯f_k(n).