First Sequence of Three Consecutive Strictly Decreasing Euler Phi Values

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Theorem

The first sequence of $3$ consecutive positive integers whose Euler $\phi$ values are strictly decreasing is:

$\map \phi {523} > \map \phi {524} > \map \phi {525}$


Proof

\(\ds \map \phi {523}\) \(=\) \(\ds 522\) Euler Phi Function of Prime
\(\ds \map \phi {524}\) \(=\) \(\ds 260\) $\phi$ of $524$
\(\ds \map \phi {525}\) \(=\) \(\ds 240\) $\phi$ of $525$




Sources