Math Origins: The Totient Function | Mathematical Association of America

Publication Date


Document Type



Leonhard Euler's totient function, ϕ(n), is an important object in number theory, counting the number of positive integers less than or equal to n which are relatively prime to n. It has been applied to subjects as diverse as constructible polygons and Internet cryptography. The word totient itself isn't that mysterious: it comes from the Latin word tot, meaning "so many." In a way, it is the answer to the question "Quot?" ("how many"?). In The Words of Mathematics, Steven Schwartzman [Sch] notes that question/answer pairings like Quo/To are common linguistic constructions, similar to the Wh/Th pairing in English ("Where? There. What? That. When? Then."). Beyond that, there are two key questions: (1) how did the notation emerge and develop, and (2) what questions was it originally intended to answer?

Publication Title


Publisher Policy

open access

Open Access Status

OA Journal

Find in your library