Euler Phi Function of 2

Theorem

$\map \phi 2 = 1$

where $\phi$ denotes the Euler $\phi$ function.


Proof

From Euler Phi Function of Prime:

$\map \phi p = p - 1$

As $2$ is a prime number it follows that:

$\map \phi 2 = 2 - 1 = 1$

$\blacksquare$


Sources

  • 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 $27$
  • 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.1$: Functions: Example $2.1.1$
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