Notes on Euler’s phi function

Abstract

We say two numbers are relatively prime if they have no prime factors in common. For n ≥ 1, the Euler’s function ϕ(n) denotes the number of positive integers not exceeding n and relatively prime to n. In this work, we state some basic propertities of the Euler’s function. That is, the behaviour of ϕ(n), relations with other multiplicative functions and solving Diophantine equations involving the expression ϕ(n).