Algebraic number

A real or complex number is called an algebraic number if it is a solution of some one-variable polynomial equation whose coefficients are all integers. All rational numbers are algebraic numbers, along with some irrational numbers. For example, the golden ratio ${\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}=1.618...}$ is a solution to the equation ${\displaystyle x^{2}-x-1=0}$. A real or complex number that is not algebraic is called transcendental.

While this is an abstract notion, theoretical mathematics has potentially far-reaching applications in communications and computer science, especially in data encryption and security.^[1]