Jäännösluokiksi
Jäännösluokiksi, known in English as residue classes or congruence classes, is a fundamental concept in abstract algebra and number theory. It arises from the process of partitioning a set of integers into subsets based on their remainders when divided by a fixed positive integer, called the modulus.
For a given modulus n, two integers a and b are said to be congruent modulo n
The equivalence classes formed by this relation are called residue classes modulo n. For a modulus n,
[0] = {..., -10, -5, 0, 5, 10, ...}
[1] = {..., -9, -4, 1, 6, 11, ...}
[2] = {..., -8, -3, 2, 7, 12, ...}
[3] = {..., -7, -2, 3, 8, 13, ...}
[4] = {..., -6, -1, 4, 9, 14, ...}
The set of all residue classes modulo n, equipped with addition and multiplication operations defined on these