Consecutive Integers with Same Euler Phi Value/Examples/15
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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:
- $\map \phi {15} = \map \phi {16} = 8$
Proof
From $\phi$ of $15$:
- $\map \phi {15} = 8$
From the corollary to Euler Phi Function of Prime Power:
- $\map \phi {16} = \map \phi {2^4} = 2^{4 - 1} = 8$
Hence the result.
$\blacksquare$