Consecutive Odd Powerful Numbers

Theorem

$25$ and $27$ are the only known pair of consecutive odd powerful numbers.

It is not known whether there are any more.


Progress

We have that:

$25 = 5^2$
$27 = 3^3$

and so by definition both are powerful.


Sources

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