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 $525$ |
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Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $523$