“residue class(modulo n)”的概念、定义、翻译、参考文献-科学参考

residue class(modulo n)

Mathematics

An equivalence class for the equivalence relation of congruence modulo n. So, two integers are in the same class if they have the same remainder upon division by n. If [a] denotes the residue class modulo n containing a, the residue classes modulo n can be represented as [0], [1], [2],…, [n−1]. The sum and product of residue classes are defined by

$[a] + [b] = [a + b], [a] [b] = [a b],$

where it is necessary to show these definitions are well defined and independent of the choice of representatives a and b. With this addition and multiplication, the set, denoted by ℤ_n, of residue classes modulo n forms a commutative ring with identity. If n is composite, the ring ℤ_n has zero-divisors, but when p is prime ℤ_p is a field.

单词	residue class(modulo n)
释义	residue class(modulo n) Mathematics An equivalence class for the equivalence relation of congruence modulo n. So, two integers are in the same class if they have the same remainder upon division by n. If [a] denotes the residue class modulo n containing a, the residue classes modulo n can be represented as [0], [1], [2],…, [n−1]. The sum and product of residue classes are defined by $[a] + [b] = [a + b], [a] [b] = [a b],$ where it is necessary to show these definitions are well defined and independent of the choice of representatives a and b. With this addition and multiplication, the set, denoted by ℤ_n, of residue classes modulo n forms a commutative ring with identity. If n is composite, the ring ℤ_n has zero-divisors, but when p is prime ℤ_p is a field.
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