residue class

[/ˈrɛzɪdjuː klɑːs/]
nounpl: residue classes
classe de resíduos
1. In modular arithmetic, the set of all integers that have the same remainder when divided by a given modulus
The residue class of 5 modulo 7 contains all integers that leave a remainder of 5 when divided by 7, such as 5, 12, 19, and -2.
A classe de resíduos de 5 módulo 7 contém todos os inteiros que deixam resto 5 quando divididos por 7, como 5, 12, 19 e -2.
2. A mathematical structure used in number theory and abstract algebra to study properties of integers under division
Working with residue classes modulo 12 helps in understanding clock arithmetic and cyclic groups.
Trabalhar com classes de resíduos módulo 12 ajuda na compreensão da aritmética de relógio e grupos cíclicos.
This is specialized mathematical terminology primarily used in academic contexts, particularly in number theory, abstract algebra, and discrete mathematics courses at universities. The concept is fundamental to modern cryptography and computer science applications. No significant regional variations exist in its usage, as it is a formal mathematical term with standardized definitions across English and Portuguese-speaking academic communities.
Synonyms / Sinônimos
congruence classremainder classequivalence class modulo n

Regional Variations

General Brazilian
classe de resíduos
Standard mathematical terminology used in universities and mathematical texts
Portugal
classe de resíduos
Same terminology, used in Portuguese mathematics education and research
USA
residue class
Common in English-language mathematics textbooks and academic discourse

Related Words

modular arithmeticmoduluscongruenceremainderequivalence relationquotient ring
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