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The word "number" is a general term which refers to a member of a given (possibly ordered) set. The meaning of "number" is often clear from context (i.e., does it refer to a ...

Number Theory

Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and ...

A theory is a set of sentences which is closed under logical implication. That is, given any subset of sentences {s_1,s_2,...} in the theory, if sentence r is a logical ...

The portion of number theory concerned with expressing an integer as a sum of integers from some given set.

Analytic number theory is the branch of number theory which uses real and complex analysis to investigate various properties of integers and prime numbers. Examples of topics ...

Algebraic number theory is the branch of number theory that deals with algebraic numbers. Historically, algebraic number theory developed as a set of tools for solving ...

Elementary number theory is the branch of number theory in which elementary methods (i.e., arithmetic, geometry, and high school algebra) are used to solve equations with ...

Computational number theory is the branch of number theory concerned with finding and implementing efficient computer algorithms for solving various problems in number ...

A formal mathematical theory which introduces "components at infinity" by defining a new type of divisor class group of integers of a number field. The divisor class group is ...