Basic Number Theory

These are the class notes for the first-semester undergraduate students of our college. These notes help students to acquire the basic knowledge of Number Theory. The pre-requisitions for reading these notes are the basic knowledge in set theory. It contains three chapters. In Chapter-I, we tried to discuss the construction of natural numbers and integers as well as the algebraic operations, ordering properties of them. Moreover, division algorithm, greatest integer functions are discussed briefly. In Chapter-II, Number theoretic functions are discussed with some well-known examples of number theoretic functions. In Chapter-III, we introduced the idea of congruences. Also, we discussed Euler's Theorem, Fermat's little theorem, Chinese remainder theorem, etc. As an application of Euler's theorem, public-key cryptosystems (RSA model) are also briefly introduced here.