Sum of five consecutive cubes is a square
Nick Hobson
nickh at qbyte.org
Sat Mar 10 15:29:30 CET 2007
Hi Seqfans,
In the Dover (2005) edition of Dickson's History of the Theory of Numbers,
Volume 2, Chapter 21, page 587, it is noted: "E. Lucas (275a) stated that
the sum of the cubes of five consecutive integers is a square only when
the middle number is 2, 3, 98 or 120."
(275a) Recherches sur l'analyse indeterminee, Moulins, 1873, 92. Extract
from Bull. Soc. d'Emulation du Departement de l'Allier, 12, 1873, 532.
The following PARI/GP script finds, additionally, middle number n = 27.
Is this sequence finite? Is such a short sequence (six terms, if we
include n = 0) worth adding to OEIS?
for(n=1, 10^8, if(issquare(5*n*(n*n+6)), print(n)))
Nick
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