Modulooperaatio

Modulo operaatio, often referred to as the modulo operation or remainder operation, is a mathematical operation that finds the remainder after division of one number by another. It is commonly represented by the percent sign (%) in many programming languages and by the word "mod" in mathematical contexts. The result of the modulo operation is always an integer.

For example, the expression 10 mod 3 equals 1. This is because when 10 is divided by 3, the quotient is 3 and the remainder is 1. Similarly, 15 mod 5 equals 0, as 15 is perfectly divisible by 5 with no remainder. The general form is a mod n, where 'a' is the dividend and 'n' is the divisor. The result is the remainder 'r' such that a = qn + r, where q is the quotient and 0 <= r < |n|.

The modulo operation has various applications in computer science and mathematics. It is frequently used in algorithms for tasks such as checking for even or odd numbers (n mod 2), cyclic operations, hashing, and cryptography. It is also fundamental in number theory and abstract algebra. In programming, it's crucial for tasks that involve wrapping around values, like in array indexing or time calculations.

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