4 Integers whose Euler Phi Value is 10,368

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Theorem

$\map \phi {25 \, 930} = \map \phi {25 \, 935} = \map \phi {25 \, 940} = \map \phi {25 \, 942} = 10 \, 368 = 2^7 \times 3^4$

where $\phi$ denotes the Euler $\phi$ function.


Proof

\(\displaystyle \map \phi {25 \, 930}\) \(=\) \(\displaystyle 10 \, 368\) $\phi$ of $25 \, 930$
\(\displaystyle \map \phi {25 \, 935}\) \(=\) \(\displaystyle 10 \, 368\) $\phi$ of $25 \, 935$
\(\displaystyle \map \phi {25 \, 940}\) \(=\) \(\displaystyle 10 \, 368\) $\phi$ of $25 \, 940$
\(\displaystyle \map \phi {25 \, 942}\) \(=\) \(\displaystyle 10 \, 368\) $\phi$ of $25 \, 942$

$\blacksquare$


The significance of this result escapes the author of this page.


Sources