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

### solved infinity relationships simple

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.

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The ( planet - little - moon ) theory

[1]-(a ^ p) + (p - a) = mod p

if a not divide p and p>a and p is prime

this law is correct in the case p = 2, 3, 5, 7 and for every prime

By mathematical induction it will be proved that it is correct for every prime p

[2]-{(a ^ p) +(p - a)} /

(a ^ (p-1)} – 1 = a + (1 / integer) This is only for p is prime and p not divides a

This is easy to be proved by mathematical induction