KiyonoKara / Number-Theory-Functions

A repository that holds some functions related to number theory.

Basic Number Theory Functions

This repository serves as a place where useful functions usually related to number theory are stored.
Please feel free to improve upon these functions or propose them.

Main Function(s)

1. Applying Number Theory to programming.
2. Cryptography with Number Theory functions.
3. Useful for finding certain answers from sets of data.

Side Note about this repository

This is NOT a library, please do not try to look for this on your package manager since it doesn't exist there.

Documentation

As a general overview, these functions primarily serve to be snippets which people can refer to.
The documentation predominantly exists here since these functions can be confusing and most definitely need some background.

As seen below, there are some core functions that will be in the documentation.

Greatest Common Divisor

This function returns the Greatest Common Divisor (GCD) based on two integers given which are a and b.

gcd = gcd(10, 20)
# Returns 10

gcd = gcd(20, 10)
# Returns 10

Note: The order of parameters do not matter.

Euclidean Algorithm

Returns the Greatest Common Divisor (GCD) as g, u and v are also returned which correspond to the equation:
ua + vb = gcd(a, b) with two given integers, a and b. There are two separate functions that return the same values but are written differently.

Returns three callable values

g, u, v = euclideanAlgorithm1(20, 30)
# Returns 10, -1, 1
#         g,   u, v

Returns an array which can still be called upon, just differently

eu = euclideanAlgorithm2(20, 30)
# Returns (10, -1, 1)
#         (g,   u, v)

Note: The order of parameters do not matter.

Documentation is still in progress, will add more to these.

Contributing

Pull requests are welcome. For bugs and/or flaws in the functions, please open an issue.

License

MIT