ABSTRACT
This chapter describes certain mathematical preliminaries. It discusses sets, functions, and basic number-theoretic topics like countability, divisibility, prime numbers, and greatest common divisor. The chapter examines basics of congruence arithmetic and the Chinese remainder theorem. It explores elementary concepts of number theory such as countability, divisibility, prime numbers, and greatest common divisor. The notion of greatest common divisor of integers is also extended to polynomials. The chapter also describes the greatest common divisor of two positive integers and the associated well-known Euclidean algorithm. This algorithm is named after the great ancient geometer, Euclid of Alexandria. The Euclidean algorithm finds the greatest common divisor of two positive integers. The extended Euclidean algorithm finds the greatest common divisor of two positive integers a and b. An extended Euclidean algorithm also exists for polynomials. This implies the existence of a Bezout’s type of result for polynomials. These in turn are useful in developing Daubechies wavelets and coiflets.
