Diophantine Analysis

Diophantine analysis is a branch of number theory focused on solving equations with whole numbers or integers. Named after the ancient mathematician Diophantus, it seeks to find integer solutions to polynomial equations, often involving multiple variables. For example, finding integer solutions to equations like x + y = 10 or x² + y² = 25. This area explores whether solutions exist, how many there are, and how to find them, blending algebra and number theory to understand the properties of integers within various equations.