Sum of Cubes of 5 Consecutive Integers which is Square/Historical Note
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Historical Note on Sum of Cubes of 5 Consecutive Integers which is Square
This result was originally published by Édouard Lucas in $1873$, where he wrote:
- The sum of the cubes of $5$ consecutive numbers is never equal to a square, except for the solutions of which the middle numbers are $2$, $3$, $27$, $98$ or $120$.
Subsequently it was reported by Leonard Eugene Dickson, who made a mistake by omitting the $27$.
The erroneous sequence is still mistakenly published on occasion.
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): $118$