Euclidean division
division with remainder of integers
Facts
8 properties- Instance of
- theorem, operation (mathematics)
- Subclass of
- division
- Defining formula
- a,b \in \mathbb{Z} \land b \neq 0 \implies \exists! q,r \mid a=bq+r \land 0 \leq r < |b|
- Described by source
- PlanetMath
- In defining formula
- a, b
- Maintained by WikiProject
- WikiProject Mathematics
- Named after
- Euclid
- Studied by
- modular arithmetic, algebra
🏷️ Also known as
en division with remainder
en Euclidean division
ar خوارزمية تقسيم
de Division mit Rest
el Ευκλείδεια διαίρεση
es division euclidea
es división euclídea
fa الگوریتم تقسیم
fi jakoyhtälö
fr division entière
fr division euclidienne
hu maradékos osztás
id Pembagian bersisa
it divisione euclidea
it teorema di divisione euclidea
it teorema di divisione in Z
ja 除法の原理
ko 나눗셈 정리
nl deling met rest
nl geheeltallige deling
🔖 Identifiers · 4
- Freebase ID
- /m/032bj_
- Larousse ID
- divers/division_euclidienne/187228
- Microsoft Academic ID (discontinued)
- 103481479
- Treccani's Enciclopedia della Matematica ID
- divisione-euclidea
🔗 Connections
Instance of 2
Studied by 2
Described by source 1
Maintained by WikiProject 1
Named after 1
Named after 1
Subclass of 1
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Summary
Euclidean division is a theorem[1].
Key Facts
- Instance of: mathematical operation[2]
- Named after: Euclid[3]
- Subclass of: division[4]
- Described by source: PlanetMath[5]
- Euclidean division's defining formula is recorded as a,b \in \mathbb{Z} \land b \neq 0 \implies \exists! q,r \mid a=bq+r \land 0 \leq r < |b|<sup id="cite-C13" class="cite-ref" title="Euclidean division — defining formula (P2534): a,b \in \mathbb{Z} \land b \neq 0 \implies \exists! q,r \mid a=bq+r \land 0 \leq r < |b|">[?].
- Studied by: modular arithmetic[6], algebra[7]
- Maintained by WikiProject: WikiProject Mathematics[8]
- In defining formula: a[9], b[10]
Body
Works and Contributions
Things named for Euclidean division include Euclidean domain[11].
Why It Matters
Entities named for it include Euclidean domain[11].