# Number Theory and Algebra for Competitive Programming

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## Topics

- Modular Arithmetic Basics [1st meet]
- Addition

- Subtraction

- Multiplication

- Division
- Explain what does modular inverse mean?

- Fermat's little theorem

- Euler's generalization of Fermat's little theorem [this includes the knowledge of phi function, so should be covered later]

- Euclidean Algorithm and its extension: GCD and LCM

- Binary Exponentiation
- Fibonacci

- Linear Diophantine Equations

- Prime Numbers
- Sieve of Eratosthenes

- Primality Tests

- Integer Factorization [this includes divisors]

- Number Theoretic Functions
- Totient Function and Euler's Generalization

- Number of divisors [lite this is basic maths]

- Sum of divisors [this also, can go over this quickly though]

### Problems

- ASC 5 Problem A (Hard)