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5. Gerald. C. F., and Wheatley. P. O., "Applied Numerical Analysis", Pearson Education, Asia, 6th
Edition, New Delhi, 2006.
6. Goyal, M, ―Computer Based Numerical and Statistical Techniques‖, Firewall
Media, New Delhi.

OMA1702 NUMBER THEORY AND APPLICATIONS L T P C
3 0 0 3
OBJECTIVES:

• This course aims at providing the necessary basic concepts of number theory and the relevant
topics of cryptography as an application of Number theory.

UNIT I DIVISIBILITY THEORY 9

Division algorithm- Base-b representations – number patterns – Prime and composite numbers –
Fibonacci and Lucas numbers – Fermat numbers

UNIT II GREATEST COMMON DIVISOR 9

Greatest Common Divisor– Euclidean Algorithm – Fundamental theorem of Arithmetic – Least
Common Multiple – Linear Diophantine Equations

UNIT III CONGRUENCE AND APPLICATIONS 9

Congruences – Linear Congruences– Divisibility tests – Modular Designs–Chinese remainder theorem
– 2x2 linear systems.

UNIT IV CLASSICAL THEOREMS 9
Wilson‘s theorem – Fermat‘s Little theorem – Pseudo Primes –Euler‘s theorem.
(theorems without proof)

UNIT V CLASSICAL CRYPTOSYSTEMS 9

Classical cryptosystems, Enciphering matrices, Public key Cryptography, RSA.

TOTAL PERIODS:45

OUTCOMES:

On completion of the course students will be able to
 use the applications of division in computations.
 apply the Euclidean Algorithm.
 solve linear Diophantine equations.
 apply the classical theorems in Number Theory.
 apply the concepts of Number Theory in cryptosystems.

Curriculum and Syllabus | Open Electives | R 2017 | REC Page 97