Last Updated：2025/12/30
Sentence
In
a
quadratic
field
Q
(√),
D
a
squarefree
integer,
with
class
number
1
any
algebraic
integer
can
be
decomposed
uniquely
into
primes
but
for
only
21
domains
Euclidean
algorithms
are
known.
We
prove
that
for
D<-19
even
remainder
sequences
with
possibly
nondecreasing
norms
cannot
determine
the
GCD
of
arbitrary
inputs.
Quizzes for review
In a quadratic field Q (√), D a squarefree integer, with class number 1 any algebraic integer can be decomposed uniquely into primes but for only 21 domains Euclidean algorithms are known. We prove that for D<-19 even remainder sequences with possibly nondecreasing norms cannot determine the GCD of arbitrary inputs.
音声機能が動作しない場合はこちらをご確認ください
English - English
Word Edit Setting
- Users who have edit permission for words - All Users
- Screen new word creation
- Screen word edits
- Screen word deletion
- Screen the creation of new headword that may be duplicates
- Screen changing entry name
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
Sentence Edit Setting
- Users who have edit permission for sentences - All Users
- Screen sentence deletion
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
Quiz Edit Setting
- Users who have edit permission for quizzes - All Users
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
