INTRODUCTION, DIVISIBILITY, PRIMES
CONGRUENCES, SOLUTIONS OF CONGRUENCES, THE CHINESE REMAINDER THEOREM- PRIME POWER MODULI, PRIME MODULUS.
PRIMITIVE ROOTS AND POWER RESIDUES-CONGRUENCES OF DEGREE TWO, PRIME MODULUS, NUMBER THEORY FROM AN ALGEBRAIC VIEW POINT , GROUPS, RINGS AND FIELDS, QUADRATIC RESIDUES.
QUADRATIC RECIPROCITY – THE JACOBI SYMBOL – GREATEST INTEGER FUNCTION.
ARITHMETIC FUNCTIONS – THE MOEBIUS INVERSION FORMULA – THE MULTIPLICATION OF ARITHMETIC FUNCTIONS –RECURRENCE FUNCTIONS
Reference Book:
1. Introduction to Analytic Number Theory by T.M. Apostol, Springer International Student Edition, Eighth Reprint, 1998, Narosa Publishing House. 2. A Classical Introduction to modern number theory by Kennath and Rosan, Second Edition, Springer, Second Indian Reprint, 2005. 3. Number Theory by George E. Andrews, Dover Publisher, 1994.
Text Book:
1. An Introduction to Theory of Numbers by Ivan Nivan and Herberts Zucherman. Fifth Edition Reprint, 2012, Wiley Eastern Limited, New Delhi. Unit-I: Chapter I : Sections 1.1 – 1.3 Unit-II: Chapter II : Sections: 2.1 – 2.7 Unit-III: Chapter II : Sections: 2.8 – 2.11 Chapters III: Section: 3.1 Unit-IV: Chapter III : Sections: 3.2, 3.3 Chapter IV: Section: 4.1 Unit-V: Chapter IV : Sections: 4.2 – 4.5
