# 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

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solved counting relationships infinity

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.

## Additional Topics

One of the most important distinctions in number theory is between prime and composite numbers. Prime numbers can only be divided evenly (with nothing left over) by 1 and themselves. Prime numbers include 2, 3, 5, 7, 11, 13, 17, and so on to infinity. The number 1 is not considered a prime. All primes are odd numbers except for 2, because any even number can be divided evenly by 2. A composite num…

Pierre de Fermat (1601-1665) is one of the most famous number theoreticians in history, but mathematics was only his hobby. He was a judge in France, and he published very little during his life. He did correspond extensively with many leading intellectuals of his day, and his mathematical innovations were presented to these pen pals in his letters. …

Karl Friedrich Gauss (1777-1855) has been called the "Prince of Mathematicians" for his many contributions to pure and applied mathematics. He was born to poor parents in Germany. His high intelligence was noticed early and nurtured by his mother and uncle, but his father never encouraged Gauss in his education. One of Gauss's most important contributions to number theory invo…

Number theory was labeled the "Queen of Mathe matics" by Gauss. For many years it was thought to be without many practical applications. That situation has changed significantly in the twentieth century with the rise of computers. Prime and composite numbers play an important role in modern cryptography or coding systems. Huge volumes of confidential information (credit card numbers,…

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## User Comments

over 6 years ago

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

please answer me and thank you