最終更新日：2025/12/08
(mathematics) In Ramsey theory, a theorem stating that, for any given positive integers r and k, there is some number N such that if the integers {1, 2, ..., N} are colored, each with one of r different colors, then there are at least k integers in arithmetic progression whose elements are of the same color.
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van der Waerden's theorem
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元となった辞書の項目
van der Waerden's theorem
固有名詞
(mathematics)
In
Ramsey
theory,
a
theorem
stating
that,
for
any
given
positive
integers
r
and
k,
there
is
some
number
N
such
that
if
the
integers
{1,
2,
...,
N}
are
colored,
each
with
one
of
r
different
colors,
then
there
are
at
least
k
integers
in
arithmetic
progression
whose
elements
are
of
the
same
color.
日本語の意味
数学・ラムゼー理論における定理で、任意の正の整数 r および k に対して、ある数 N が存在し、1,2,...,N の整数が r 種の色で彩色された場合、同じ色で塗られた等差数列を形成する k 個以上の整数が必ず存在することを保証する定理
意味（1）
(mathematics)
In
Ramsey
theory,
a
theorem
stating
that,
for
any
given
positive
integers
r
and
k,
there
is
some
number
N
such
that
if
the
integers
{1,
2,
...,
N}
are
colored,
each
with
one
of
r
different
colors,
then
there
are
at
least
k
integers
in
arithmetic
progression
whose
elements
are
of
the
same
color.
