- #1
rashida564
- 220
- 6
- TL;DR Summary
- Find a ∈ Z such that a^6 ≡ a mod 6
Hi everyone, I can find multiple of number for example 2,3,4 and so on. But is there any reason why those number does work.
Where did you see try and error? Factorization to investigate factors is a quite natural thing.rashida564 said:Is it try and error method?
Modular arithmetic is a branch of mathematics that deals with operations on integers, where the result is always within a fixed range. It involves finding the remainder after dividing two numbers, also known as the modulus.
Modular arithmetic has many practical applications, including cryptography, computer science, and music theory. It can also be used to solve problems involving repeating patterns, such as finding the day of the week for a given date.
To find multiples in modular arithmetic, you can multiply a number by any integer and then take the remainder when divided by the modulus. For example, in modular arithmetic with a modulus of 5, the multiples of 3 would be 3, 6, 9, 12, etc. with remainders of 3, 1, 4, 2, respectively.
The reasoning behind modular arithmetic lies in the concept of congruence, which means that two numbers have the same remainder when divided by a given modulus. This allows for efficient calculations and simplification of complex problems.
Modular arithmetic is closely related to clock arithmetic, as both involve finding the remainder after division by a fixed number. In clock arithmetic, the modulus is typically 12 or 24, representing the hours on a clock, while in modular arithmetic, the modulus can be any positive integer.