Smallest 5th Power equal to Sum of 5 other 5th Powers/Mistake

Source Work

1986: David Wells: Curious and Interesting Numbers:

The Dictionary

$72$

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary

$72$

Mistake

$72^5 = 19^5 + 43^5 + 46^5 + 47^5 + 67^5$ is the smallest $5$th power equal to the sum of $5$ other $5$th powers.

Correction

Refuted by:

\(\ds 1^5\)

\(=\)

\(\ds 1^5 + 0^5 + 0^5 + 0^5 + 0^5\)

\(\ds = 1^5 + 5^5 + \paren {-5}^5 + 17^5 + \paren {-17}^5\)

\(\ds 2^5\)

\(=\)

\(\ds 2^5 + 0^5 + 0^5 + 0^5 + 0^5\)

\(\ds = 2^5 + 31^5 + \paren{-31}^5 + 97^5 + \paren{-97}^5\)

What it should say is something more like:

$72^5 = 19^5 + 43^5 + 46^5 + 47^5 + 67^5$ is the smallest positive $5$th power equal to the sum of $5$ other distinct positive $5$th powers.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $72$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $72$