Number theory is a branch of mathematics that deals with properties of numbers and their relationships. It has several synonyms that are used interchangeably to refer to it. One such synonym is arithmetic theory which accounts for basic operations like addition, subtraction, multiplication, and division. Another synonym is the theory of numbers, which emphasizes the study of prime numbers, number patterns, and relationships between different numbers. Algebraic number theory, a branch that deals with algebraic structures and their relationship to numbers, is also considered a synonym for number theory. Lastly, analytic number theory is another synonym which uses methods from calculus and analysis to study number-theoretical questions.