ABSTRACT
Throughout the school curriculum, an emphasis is placed on numbers, their properties, and relationships between and among them. This chapter presents some of the basics of number theory that middle school and secondary school teachers should be aware of. It then considers interesting applications that range from recreational areas such as numerical curiosities and tricks, to such serious practical applications as the workings of a computer and high-level security systems. Knowing that there are infinitely many primes, and that there can be very large gaps between a prime and the next prime, led mathematicians to wonder about the distribution of primes. One of the fundamental topics stressed throughout the middle and secondary school curriculum is the greatest common divisor or greatest common factor of two numbers a and b. A rather sophisticated and very important application of modular arithmetic is RSA encryption.
