Euler's totient function is a mathematical concept that calculates the number of positive integers that are less than a given number and coprime to that number. There are several synonyms for this function, such as Euler's phi function, Euler's totient, and Euler's totient phi. The function is named after its discoverer, the Swiss mathematician Leonhard Euler, who first introduced it in 1763. This function is widely used in number theory and cryptography, and has applications in various fields such as computer science, engineering, and physics. Overall, the Euler's totient function is a crucial tool in understanding complex mathematical concepts, and its synonyms are used interchangeably in academic literature.