Definition:Euler Phi Function/Also known as
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Euler Phi Function: Also known as
The Euler $\phi$ function is also known as:
- the totient function
- the Euler totient function.
It is also variously rendered:
- with a hyphen: Euler $\phi$-function
- in the possessive form: Euler's $\phi$ function
- merely as Euler's function
- the $\phi$ function
The symbol $\map \varphi n$ can sometimes be seen.
Some sources use the term indicator function, but this has more than one use, and so is discouraged on $\mathsf{Pr} \infty \mathsf{fWiki}$.
Sources
- 1964: Walter Ledermann: Introduction to the Theory of Finite Groups (5th ed.) ... (previous) ... (next): Chapter $\text {I}$: The Group Concept: $\S 6$: Examples of Finite Groups: $\text{(iii)}$
- 1967: John D. Dixon: Problems in Group Theory ... (previous) ... (next): Introduction: Notation
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {4-2}$ Residue Systems: Definition $\text {4-5}$
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $1$: Properties of the Natural Numbers: $\S 25$
- 1976: Tom M. Apostol: Introduction to Analytic Number Theory ... (previous) ... (next): $2.3$: The Euler totient function $\map \varphi n$
- 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): $\S 2.3$: Congruences
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Euler phi function or totient
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.4$: Integer Functions and Elementary Number Theory: Exercise $27$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): phi function (totient function)
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): totient function
- 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.1$: Functions: Example $2.1.1$
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Euler's phi function (phi function, totient function)
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Euler's function