ABSTRACT
The field of number theory occupies a distinguished spot within mathematics: the German mathematician Carl Friedrich Gauss even dubbed it the "Queen of Mathematics." The most fundamental concept in number theory is probably divisibility. According to the Fundamental Theorem of Number Theory, every integer prime or can be expressed as a product of positive primes; furthermore, this factorization into primes is essentially unique. The prime and prime-power factorizations of integers are very useful. The branch of number theory commonly referred to as multiplicative number theory deals with the various ways that integers can be factored into products of other integers. In contrast to multiplicative number theory that deals with ways in which positive integers factor into products of other positive integers, additive number theory is concerned with ways those positive integers can be expressed as sums of certain other positive integers.
