4 Integers whose Euler Phi Value is 10,368

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

\(\ds \map \phi {25 \, 930}\)

\(=\)

\(\ds 10 \, 368\)

$\phi$ of $25 \, 930$

\(\ds \map \phi {25 \, 935}\)

\(=\)

\(\ds 10 \, 368\)

$\phi$ of $25 \, 935$

\(\ds \map \phi {25 \, 940}\)

\(=\)

\(\ds 10 \, 368\)

$\phi$ of $25 \, 940$

\(\ds \map \phi {25 \, 942}\)

\(=\)

\(\ds 10 \, 368\)

$\phi$ of $25 \, 942$

$\blacksquare$

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

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $25,930$