Utkal University, Odisha, Mathematics Semester 6, NUMBER THEORY Syllabus

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Unit - 1 Linear Diophantine Equation

Unit 1

Linear Diophantine equation

1.1 Linear Diophantine equation

1.2 Prime counting function

1.3 Statement of prime number theorem

1.4 Goldbach conjecture

1.5 Linear congruences

1.6 Complete set of residues

1.7 Chinese remainder theorem

1.8 Fermats little theorem

1.9 Wilsons theorem

Unit - 2 Number Theoretic Functions

Unit 2

Number theoretic functions

2.1 Number theoretic functions

2.2 Sum and number of divisors

2.3 Totally multiplicative 1’

2.4 Functions definition and properties of the Dirichlet product

2.5 The Mobius inversion formula

2.6 The greatest integer function

2.7 Eulers phifunction Eulers theorem some properties of Eulers phifunction.

2.8 Reduced set of residues

Unit - 3 Order Of An Integer Modulo N

Unit 3

Order of an integer modulo

3.1 Order of an integer modulo n

3.2 Primitive roots for primes composite numbers having primitive roots

3.3 Eulers criterion

3.4 The Legendre symbol Jacobi symbol and their properties

3.5 Quadratic reciprocity

3.6 Quadratic congruences with composite moduli

Unit - 4 Affine Ciphers

Unit 4

Affine ciphers

4.1 Affine ciphers Hill ciphers

4.2 Public key cryptography RSA encryption and decryption

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Other Subjects of Semester-6
Group theory ii
Complex analysis
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