Hello guys,

I am writing about most of the mathematics topics involved in competitive Programming.

GCD (Greatest Common Divisor)

Properties of GCD

Brute Force and Euclidean algorithm to compute GCD

Analysis of Euclidean algorithm

Modular Arithmetic

Basic properties of modulo

proof of condition for inverse modulo to exist

Modulo inverse using extended euclidean algorithm with proof

Modulo inverse using Fermat’s theorem

Solution of Modulo inverse of all integers less than m

Prime Numbers

Properties of prime

Wilson’s theorem

School method for primality testing

Fermat’s theorem and its drawbacks

Miller-Rabin test with proof

Why Miller-Rabin is better

Deterministic version of Miller-Rabin

Seive of Eratosthenes

Prime Factors

Properties of Prime Factors

Proof of Number of divisors

Trial Division Method for Prime Factors

Optimization for trial Division method

O(N^{1/3}) algorithm for calculating number of divisors

Logarithmic Prime Factorisation Using Seive

Combinatorics (coming soon)

Probability (coming soon)

Geometry (coming soon)

Miscellaneous topics (coming soon)

Please tell me if something is wrong or you would like me to add some more information.

Thank you and Happy Coding