Last Updated
：2025/11/29
abc conjecture
Noun
(number
theory)
Given
coprime
positive
integers
a,
b
and
c,
such
that
a
+
b
=
c,
and
d
the
radical
of
abc
(the
product
of
its
distinct
prime
factors),
the
conjecture
that
d
is
usually
not
much
smaller
than
c
(in
other
words,
that
if
a
and
b
are
divisible
by
large
powers
of
primes,
then
c
usually
is
not).
Japanese Meaning
abc予想とは、互いに素な正整数 a, b, c（a + b = c）に対し、abc の異なる素因数の積である「d」が通常 c よりもあまり小さくならない、という数論上の予想です。 / つまり、a や b に大きな素数の高いべきが含まれている場合には、c も通常大きくなるという性質を示唆しています。
Sense（1）
(number
theory)
Given
coprime
positive
integers
a,
b
and
c,
such
that
a
+
b
=
c,
and
d
the
radical
of
abc
(the
product
of
its
distinct
prime
factors),
the
conjecture
that
d
is
usually
not
much
smaller
than
c
(in
other
words,
that
if
a
and
b
are
divisible
by
large
powers
of
primes,
then
c
usually
is
not).
Sense（2）
（ plural ）
Quizzes for review
(number theory) Given coprime positive integers a, b and c, such that a + b = c, and d the radical of abc (the product of its distinct prime factors), the conjecture that d is usually not much smaller than c (in other words, that if a and b are divisible by large powers of primes, then c usually is not).
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See correct answer
abc conjecture
Many mathematicians are fascinated by the abc conjecture because it links the sizes of a, b, and c to the radical of abc in deep and unexpected ways.
See correct answer
Many mathematicians are fascinated by the abc conjecture because it links the sizes of a, b, and c to the radical of abc in deep and unexpected ways.
音声機能が動作しない場合はこちらをご確認ください
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