Abstract
This chapter focuses on the elementary number theory. It emphasizes on all integers, which may be positive, negative, and zero. The set in a number theory is denoted by, Z = {0, ±1, ±2, ±3, …} and whenever one writes any of the symbols a, b, c, d, ……, x, y, z, …. the symbols will represent the elements of Z. When it is given a, b ∈ Z with a ≠ 0, one can say that a divides b when there exists c ∈ Z such that ac = b. It should be noted that the statement a|b includes the fact that a ≠ 0; thus, according to the definition, 0 does not divide any integer. For a ≠ 0, one notes that the integers a and –a are distinct, with one of them positive and the other negative. When it is given a, b ∈ Z with a > 0, then a may divide b or it may not; however, there always exists an expression for b in terms of a, and this expression also settles the question of divisibility. An integer p > 1 is said to be prime when 1 and p are its only positive divisors; if p > 1 is not prime, then it is a composite number. Every integer greater than 1 can be expressed as a finite product of primes.
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