English Dictionary

Dickson's conjecture

固有名詞

(number theory) The conjecture that, for a finite set of linear forms a₁ + b₁n, a₂ + b₂n, ..., aₖ + bₖn with bᵢ ≥ 1, there are infinitely many positive integers n for which they are all prime, unless there is a congruence condition preventing this.

日本語の意味

（数論）ディクソン予想。具体的には、各bᵢが1以上である有限個の一次式 a₁ + b₁n, a₂ + b₂n, …, aₖ + bₖn において、特定の合同条件によって成立が妨げられない場合、これらすべてが素数となる正の整数 n が無限に存在するという予想。

Although unproven, Dickson's conjecture has motivated extensive research into when several linear forms a₁ + b₁n, a₂ + b₂n, ..., a_k + b_kn can all be prime simultaneously.

未証明ではあるが、ディクソンの予想は複数の一次式 a₁ + b₁n、a₂ + b₂n、…、a_k + b_kn が同時に素数になる場合に関する多くの研究を促してきた。

意味（1）

(number theory) The conjecture that, for a finite set of linear forms a₁ + b₁n, a₂ + b₂n, ..., aₖ + bₖn with bᵢ ≥ 1, there are infinitely many positive integers n for which they are all prime, unless there is a congruence condition preventing this.