Consecutive Integers with Same Euler Phi Value/Examples/164
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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:
- $\map \phi {164} = \map \phi {165} = 80$
Proof
From $\phi$ of $164$:
- $\map \phi {164} = 80$
From $\phi$ of $165$:
- $\map \phi {165} = 80$
Hence the result.
$\blacksquare$