OFFSET
1,1
COMMENTS
The only primitive terms (that is, in which the summands do not all have a common factor) known are 144 and 85359. - Jianing Song, Jan 24 2020
The paper by Lander and Parkin where they just give the first known counterexample to Euler's conjecture, 27^5 + 84^5 + 110^5 + 133^5 = 144^5, found using a CDC6600, is known as one of the shortest published proofs. - M. F. Hasler, Mar 11 2020
REFERENCES
L. E. Dickson, History of the theory of numbers, Vol. 2, Chelsea, New York, 1952, p. 648.
LINKS
L. J. Lander and T. R. Parkin, Counterexample to Euler's conjecture on sums of like powers, Bull. Amer. Math. Soc. 72 (6) (1966), p. 1079.
Burkard Polster, Euler's and Fermat's last theorems, the Simpsons and CDC6600, Mathologer video (2018).
Wikipedia, Euler's sum of powers conjecture
EXAMPLE
a(1) = 144 because 144^5 = 27^5 + 84^5 + 110^5 + 133^5;
a(593) = 85359 because 85359^5 = 55^5 + 3183^5 + 28969^5 + 85282^5 = 4531548087264753520490799 (Jim Frye 2005). [Typo corrected by Sébastien Palcoux, Jul 05 2017]
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Oct 21 2007
EXTENSIONS
Incorrect formula removed by Jianing Song, Jan 24 2020
STATUS
approved