Diophantine Analysis is a branch of number theory that focuses on finding integer solutions to polynomial equations. Named after the ancient Greek mathematician Diophantus, it studies equations where the variables are constrained to whole numbers. This area of mathematics explores various types of equations, including linear and quadratic forms, and seeks to determine whether solutions exist and how many there are. One of the key concepts in Diophantine Analysis is the Diophantine equation, which is an equation that requires integer solutions. Famous examples include Fermat's Last Theorem and the Pell's equation. Researchers use various techniques, such as modular arithmetic and algebraic geometry, to analyze these equations and uncover their properties.