Techniques Overview

Here's what you'll learn:

$1.$ Euler's totient $\phi(n)$ counts integers coprime to $n$. Use it for counting and modular inverse.

$2.$ Chinese Remainder Theorem combines modular constraints into a single equation.

$3.$ Prime factorization via GCD between numbers.

$4.$ Diophantine equations: $ax + by = c$ has solutions iff $\gcd(a, b)$ divides $c$.