Consecutive Integers with Same Euler Phi Value/Examples/104

Example of Consecutive Integers with Same Euler Phi Value

Let $\phi: \Z_{>0} \to \Z_{>0}$ denote the Euler $\phi$ function: the number of strictly positive integers less than or equal to $n$ which are prime to $n$.

Then:

$\map \phi {104} = \map \phi {105} = 48$

Proof

From $\phi$ of $104$:

$\map \phi {104} = 48$

From $\phi$ of $105$:

$\map \phi {105} = 48$

Hence the result.

$\blacksquare$

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $104$