In mathematics, the result of the modulo operation is an equivalence class, and any member of the class may be chosen as
In … See more

Some calculators have a mod() function button, and many programming languages have a similar function, expressed as mod(a, n), for example. Some also support expressions that use "%", "mod", or "Mod" as a modul… See more

When the result of a modulo operation has the sign of the dividend (truncated definition), it can lead to surprising mistakes.
For example, to test if an integer is odd, one might be in… See more

Modulo operations might be implemented such that a division with a remainder is calculated each time. For special cases, on some hardware, faster alternatives exist. For example, the modulo of powers of 2 can alternativel… See more

Some modulo operations can be factored or expanded similarly to other mathematical operations. This may be useful in cryptography proofs, such as the Diffie–Hellman key exchange. The properties i… See more

Sometimes it is useful for the result of a modulo n to lie not between 0 and n − 1, but between some number d and d + n − 1. In that case, d is called an offset and d = 1 is particularly common.
There doe… See more