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In le mathematica , un classe de congruentia [ 1]
a
+
m
Z
,
{\displaystyle a+m\mathbb {Z} ,}
a
{\displaystyle a}
modulo un numero
m
{\displaystyle m}
insimul de omne numeros que lassa le mesme residu como
a
{\displaystyle a}
division per
m
{\displaystyle m}
classe de residuo .
(
n
Z
,
+
)
{\displaystyle (n\mathbb {Z} ,+)}
subgruppo del gruppo abelian
(
Z
,
+
)
{\displaystyle (\mathbb {Z} ,+)}
n
∈
N
{\displaystyle n\in \mathbb {N} }
subgruppo normal . Le gruppo quotiente
Z
n
:=
Z
/
n
Z
{\displaystyle \mathbb {Z} _{n}:=\mathbb {Z} /n\mathbb {Z} }
gruppo de classes de congruentia modulo
n
{\displaystyle n}
. Illo es le anello de numeros integre modulo
n
{\displaystyle n}
n
{\displaystyle n}
[
a
]
n
:=
[
a
]
:=
a
+
n
Z
=
{
a
+
m
|
m
∈
n
Z
}
=
{
a
+
n
z
|
z
∈
Z
}
{\displaystyle [a]_{n}:=[a]:=a+n\mathbb {Z} =\{a+m\ |\ m\in n\mathbb {Z} \}=\{a+nz\ |\ z\in \mathbb {Z} \}}
es se nomina classes de congruentia relative al addition modulo
n
{\displaystyle n}
Z
/
n
Z
=
{
[
0
]
,
[
1
]
,
…
,
[
n
−
1
]
}
{\displaystyle \mathbb {Z} /n\mathbb {Z} =\{[0],[1],\ldots ,[n-1]\}}
Le operation interne de
Z
/
n
Z
{\displaystyle \mathbb {Z} /n\mathbb {Z} }
+
{\displaystyle +}
Per exemplo, in
Z
/
5
Z
{\displaystyle \mathbb {Z} /5\mathbb {Z} }
[
3
]
5
+
[
4
]
5
=
[
3
]
+
[
4
]
=
[
2
]
=
[
2
]
5
{\displaystyle \ [3]_{5}+[4]_{5}=[3]+[4]=[2]=[2]_{5}}
proque
3
+
4
=
7
=
2
+
5
{\displaystyle 3+4=7=2+5}
(
3
+
4
)
+
5
Z
=
7
+
5
Z
=
2
+
5
Z
{\displaystyle (3+4)+5\mathbb {Z} =7+5\mathbb {Z} =2+5\mathbb {Z} }
↑
Derivation (in ordine alphabetic):
(ca ) ||
(de) Restklasse ||
(en) (es) (fr) (it) (pt) (ro )
|| (ru) Класс вычетов
![{\displaystyle [a]_{n}:=[a]:=a+n\mathbb {Z} =\{a+m\ |\ m\in n\mathbb {Z} \}=\{a+nz\ |\ z\in \mathbb {Z} \}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/090ee5874bb2de99fb9188efa02c415683e4ab30)
![{\displaystyle \mathbb {Z} /n\mathbb {Z} =\{[0],[1],\ldots ,[n-1]\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7086e2868eb6d01cc1f9bfd4722550f02ca3af15)
![{\displaystyle \ [3]_{5}+[4]_{5}=[3]+[4]=[2]=[2]_{5}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ffdfc76d2f1ca80f9e245577e4459ed97c45d846)
