Euler Phi Function of n equal to Euler Phi Function of n+3

Theorem

Let $\phi$ denote the Euler $\phi$ function.

The only solutions to the equation:

$\map \phi n = \map \phi {n + 3}$

less than $1 \, 000 \, 000$ are:

$\map \phi 3 = \map \phi 6 = 2$

$\map \phi 5 = \map \phi 8 = 4$

Proof

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Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3$