最終更新日：2025/12/07
(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).
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Schinzel's hypothesis H
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元となった辞書の項目
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
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).
