Sum of Cubes of 5 Consecutive Integers which is Square/Mistake

Source Work

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

The Dictionary

$118$

Mistake

The sum of the cubes of the $5$ consecutive positive integers $118$ to $122$ is a square.

The only other similar sequences with this property start with $1$ and $96$.

Correction

$25$ also has that property.

Édouard Lucas published this result in $1873$.

However, when Leonard Eugene Dickson reported on it in his History of the Theory of Numbers, Volume II of $1920$, he appears to have erroneously omitted the sequence starting with $25$.

The correct sequence appears on On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008): A126203.

The erroneous sequence is documented on On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008): A128931.

Sources

• 1873: E. Lucas: Recherches sur l'analyse indéterminée (Bull. Soc. d'Emulation du Departement de l'Allier Vol. 12: p. 532)

• 1920: Leonard Eugene Dickson: History of the Theory of Numbers: Volume $\text { II }$: Chapter $21$

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $118$