- #1
JJKorman1
- 4
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I understand how to solve: a=12mod7 => a = 5, I think, however,
how do you solve for a=7mod12 ?
Stumped
how do you solve for a=7mod12 ?
Stumped
Integers Modulo n, also known as modular arithmetic, is a mathematical concept that deals with the remainder of division of integers by a positive integer n. It is denoted by the symbol "mod", and is used to find patterns and solutions in number systems.
Modular arithmetic has many practical applications, such as in clock systems, calculating interest rates, and cryptography. It can also be used in computer programming to efficiently store and manipulate data.
The properties of Integers Modulo n include closure, commutativity, associativity, distributivity, and identity. This means that when performing operations on integers modulo n, the result will always be another integer modulo n, and the order of operations does not matter.
The inverse of an integer modulo n can be calculated using the extended Euclidean algorithm. This algorithm finds the greatest common divisor of two integers and uses it to calculate the inverse. Alternatively, the inverse can also be found by trial and error using the modular multiplicative inverse property.
No, not every integer has a modular inverse. An integer a only has a modular inverse modulo n if it is coprime to n, meaning that they share no common factors other than 1. If a and n are not coprime, then the inverse does not exist.