Number Theory is the examination of integers. It is also sometimes called “Higher Arithmetic” because it is a discipline of pure mathematics which studies properties and rules of whole numbers. Some of the most prominent constituents of Number Theory are Prime Numbers and Prime Factorization. Although Number Theory addresses many disciplines in Mathematics, in Algebra, it specifically refers to the study of the algebraic properties of mathematical objects of interest. For example, in the following equation:

X^2+3x+2 = 0

The unknown x is referred to as an algebraic number, as there may not be one specific value associated with it. Thus, it is can be viewed as a generalization for a specific set of rational numbers within the context of the equation. The equation above can be solved using the quadratic equation or more simply, by factorization:

X^2+3x+2 = 0

(x+2)(x+1) = 0

X = -1, -2

Thus, through factorization, it can be seen that x is not just one value, but rather it can be two: x = -1 and x = -2. Thus, Number Theory in Algebra is concerned with evaluating the properties of x, and by extension, unknown variables that can generalize rational numbers.