Jäännösluku

Jäännösluku, often translated as "remainder" or "residue" in English, is a fundamental concept in number theory and arithmetic. When an integer is divided by another non-zero integer, the jäännösluku is the amount that is left over after performing the division as many times as possible. For example, when 10 is divided by 3, the quotient is 3 and the jäännösluku is 1, because 10 = 3 * 3 + 1.

The concept of jäännösluku is closely related to modular arithmetic. In modular arithmetic, we are interested in the remainders of divisions. For instance, "10 mod 3" is equal to 1, signifying that 10 and 1 have the same remainder when divided by 3. This means they belong to the same congruence class modulo 3.

The jäännösluku plays a crucial role in various mathematical fields and practical applications. It is used in cryptography, for instance, in algorithms like RSA, where operations involving remainders are essential for secure communication. In computer science, modulo operations are frequently used for tasks such as hashing, generating pseudo-random numbers, and managing data structures like circular arrays. The properties of jäännösluvut are formally described by the division algorithm, which states that for any integers a (dividend) and b (divisor) with b non-zero, there exist unique integers q (quotient) and r (remainder) such that a = bq + r, and 0 <= r < |b|.