Sums of two squares

This thesis shows that the properties of integers and rings of Gaussian integers have analogous properties. Many basic concepts in abstract algebra like groups, fields, ring and integral domains are included. Moreover, the concepts of divisibility and congruences of number theory also play a major role in this study.The main result of this study is that an integer is the sum of two non-zero squares in integers if each element of integers of the form a = 2em2n, where, m is a product of primes congruent to 3 mod 4, n is a product of primes congruent to 1 mod 4 and where either n 1 or n is odd