Author(s) :

K Madhumitha .

Volume/Issue :

Abstract :

ABSTRACT: Number the ory is a Branch of Mathematics that focuses on the properties and relationships of integers. It is one of the oldest and most fundamental areas of mathematics, with roots dating back to ancient times. Number Theory explores concepts such as prime numbers, divisibility, modular arithmetic, and Diophantine equations. The applications of number theory are diverse and impact various fields beyond pure mathematics. For instance, in cryptography, number theory forms the basis for encryption algorithms such as RSA, which relies on the difficult of factoring large composite numbers into primes. Number theory also plays a crucial role in coding theory, where it helps design error-corecting codes and efficient data transmission methods. Additionally, in computer science, algorithms based on number theoretic principles are used in tasks ranging from primality testing to optimization. Overall, Number theory not only enriches our understanding of the properties of integers but also underpins numerous practical applications essential to modern technology and communication. These abstract underscores the foundational significance and practical application of number theory in contemporary mathematics. KEYWORDS Integer, Prime, GCID, LCM, Reminder, Divisor, Divide, RSA, Cryplography, Algebraic Numnber Theory. Euclidean Algorithm, Chinese Remainder Theorem, Quadratic Residues, Fermat's Theorems, Number Theoretic Functions, Diophantine Equations, Congruences, Modular Arithmetic.

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