Advanced Concepts in Number Theory 🧮

Modular Arithmetic 🔄

Modular arithmetic is a system of arithmetic for integers, which considers the remainder. It is incredibly useful in cryptography, computer science, and many mathematical proofs.

Quadratic Residues ✅

A quadratic residue modulo n is an integer q such that there exists an integer x with the property x² ≡ q (mod n). This concept is vital in areas such as cryptographic protocols and algorithm design.

Fermat's Last Theorem 💡

Fermat's Last Theorem states that there are no whole number solutions to the equation xⁿ + yⁿ = zⁿ for n greater than 2. It was proven by Andrew Wiles in 1994, an achievement that captivated the world.