Euclid's Theorem and Its consequence

Set of integers is denoted by Z and defined as:

Z = {0,±1, ±2, ±3,...}

Z+ = {1, 2, 3, ...}

Z- = {-1, -2, -3, ...}

Z = {0, -1, -2, -3, ...}

Z = {0, 1, 2, 3, ...}

In non-positive and non-negative integer, we cannot denote them by Z+ and Z- respectively.

Let a,b belongs to Z, then b is said to be divisible by a, where a does not equal to 0(Zero) if c belongs to Z, exist. Such that

Where a is called divisor or factor of b and b is called multiple of a.

Symbolically, we write a | b, if a divides b and a.

Euclid's Theorem and Its consequence

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