ABSTRACT
Quite simply, number theory is the study of numbers, where the primary focus is on the integers. Besides learning the basics of number theory, this chapter aims to gain more experience with the proof techniques. It explores some consequences of a less elementary but extremely important property. For a useful application of the Well-Ordering Principle, the chapter revisits the integer division taught in elementary school. In addition to learning some of the basics in the beautiful area of number theory, it shows some interesting applications. The check digits appended to the ends of identification numbers are discussed. The chapter considers error-correcting codes, which enable messages to be read despite the possible introduction of errors during transmission. To send secret messages, it considers linear ciphers. The chapter describes powerful public key encryption method known as RSA encryption is introduced.
