NUMBER THEORY:
The branch of mathematics that deals with properties and relationship of numbers mainly concerned with positive integers.
HISTORY OF NUMBER THEORY:
Number theory is one of the oldest branches of mathematics. Many mathematicians contributed to its development by searching for solution of easy-to-formulate problems. Some of which are:
EUCLID OF ALEXANDRIA summarized in his ELEMENTS the contemporary ancient knowledge of mathematics.it consists of thirteen books, two of which (Book 7 and Book 9) are dedicated to number theory. These two books include theorems related to classical number theory.
DIOPHANTUS OF ALEXANDRIA also wrote a treatise consisting of thirteen books, the last 7 of which were discovered only in 1973.The books deal with the solution of integer-valued equation, which were named after him as Diophantine equations.
MUHAMMAD IBN MUSA AL-KHWARIZMI developed many methods of arithemetics, which is underlying the number theory.
The theory CONGRUENCES AND MODULAR ARITHEMETIC was first developed by CARL FREDRICH GAUSS. A milestone in the development of number theory was his book Disquistiones arithmeticae, published in 1801,which was written by Gauss.
For long time, number theory was considered a “pure” branch of mathematics, i.e. without any practical applications.
NUMBER THEORY USES:
Number theory is the prime source to show that numbers can be fascinating.
Number theory opens the door to many mathematicals conjectures.
Number theory provides an avenue to extend and practice mathematical skills.
Number theory offers a source of recreations.
APPLICATIONS OF NUMBER THEORY IN DIFFERENT FIELDS
Numerous divisibility tests employ number theory to determine whether a given integer, "m," is divisible with the integer, "n." This theory is employed not just in mathematics but also in coding, security systems, e-commerce websites, device authentication, and many more fields
Example: Find the Greatest Common Divisor (GCD) of the numbers 40 and 70.
Solution: Divisors (factors) of the number 40 are 1, 2, 4, 5, 8, 10, 20, 40.
Divisors (factors) of the number 70 are 1, 2, 5, 7, 10, 14, 35, 70.
The Greatest Common Divisor in 40 and 70 is 10.
Therefore, the GCD of 40 and 70 is 10.
NUMBER THEORY FOR DIGITAL CASH: The whole of encryption works due to number theory. As result, security of transaction is ensured. If it were not for number theory, your money will not be safe in your bank, information about you could be accessed by anyone.
ERROR-CORRECTING CODE: An error-correcting code is an algorithm for expressing a sequence of numbers such that any errors which are introduced can be detected and corrected based on the remaining numbers.
PUBLIC KEY CRYPTOGRAPHY: Public key cryptography, including the RSA algorithm, is the most well-known application of number theory. Many technologies we take for granted, including the capacity to conduct secure online transactions, are made possible by public key cryptography.
