Around 600 B.C., Pythagoras and his disciples made rather thorough study of integers. They were the first to classify integers in various ways, such as even numbers, odd numbers, prime numbers and composite numbers. This chapter explores the Fundamental theorem of Arithmetic. After Euclid in 300 B.C., no significant advances were made in number theory until about A.D. 250. In the 17th century, the subject was revived in Western Europe, largely through the efforts of a remarkable French Mathematician Pierre de Fermat, who is generally acknowledged to be the father of Modern Number Theory. “Equivalence relation” is a tool for abstraction. Real applications are to algebric structures that are rather complex.