# Number Theory

## Prime And Composite Numbers, Fermat's Theorem, Gauss And Congruence, Fermat's Failed Prime Number FormulaFamous formulas in number theory, Famous problems in number theory

Number theory is the study of natural, or counting numbers, including prime numbers. Number theory is important because the simple sequence of counting numbers from one to infinity conceals many relationships beneath its surface.

Number theory is full of famous formulas that illustrate the relationships between whole numbers from 1 to infinity. Some of these formulas are very complicated, but the most famous ones are very simple, for example, the theorem by Fermat below that proves if a number is prime.

Number theory is an immensely rich area and it is defined by the important problems that it tries to solve. Sometimes a problem was considered solved, but years later the solution was found to be flawed. One important challenge in number theory has been trying to find a formula that will describe all the prime numbers. To date, that problem has not been solved. Two of the most famous problems in number theory involve Fermat.