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About
Bezout's lemma (number theory)
(Theorem)
Let
be
integers
, not both zero. Then there exist two integers
such that:
This does not only work on
but on every
integral domain
where an
Euclidean valuation
has been defined.
"Bezout's lemma (number theory)" is owned by
mathwizard
.
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See Also:
Euclid's algorithm
,
Euclid's coefficients
Other names:
Bezout's lemma, Bezout's theorem
Attachments:
proof of Bezout's Theorem
(Proof)
by Thomas Heye
corollary of Bézout's lemma
(Theorem)
by pahio
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Cross-references:
Euclidean valuation
,
integral domain
,
integers
There are
7 references
to this entry.
This is
version 7
of
Bezout's lemma (number theory)
, born on 2002-05-27, modified 2004-02-13.
Object id is
2954
, canonical name is
BezoutsLemma
.
Accessed 11164 times total.
Classification:
AMS MSC
:
11A05
(Number theory :: Elementary number theory :: Multiplicative structure; Euclidean algorithm; greatest common divisors)
Pending Errata and Addenda
None.
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forum policy
Bezout's lemma?
by
NeuRet
on 2002-05-27 16:46:52
I have always known this entry as the Euclidean
algorithm. Not that I want to be greedy, but shouldn't this result go directly under the Euclidean algorithm, and in that entry, perhaps, mention this alternative name for it?
[
reply
|
up
]
Re: Bezout's lemma?
by mathwizard
on 2002-05-27 17:26:36
Re: Bezout's lemma?
by NeuRet
on 2002-05-27 20:32:12
Re: Bezout's lemma?
by drini
on 2002-05-27 23:33:18
Re: Bezout's lemma?
by mathwizard
on 2002-05-28 09:18:35
Re: Bezout's lemma?
by vitriol
on 2002-05-28 06:35:14
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