492 is Sum of 3 Cubes in 3 Ways/Historical Note

Historical Note on 492 is Sum of 3 Cubes in 3 Ways

Andreas-Stephan Elsenhans and Jörg Jahnel reported in $2009$ on a systematic investigation they performed on all the solutions to the equation:

$x^3 + y^3 + z^3 = n$

for all $0 < n < 1000$ and such that $\size x, \size y, \size z \le 10^{14}$.

Within that range, they discovered that there are exactly $3$ solutions for $n = 492$.

Of all the numbers from $0$ to $1000$, most have many more than $3$ such ways, although a few still have no known solutions.

The full results can be found at https://www.uni-math.gwdg.de/jahnel/Arbeiten/Liste/threecubes_20070419.txt.

Sources

• April 2009: Andreas-Stephan Elsenhans and Jörg Jahnel: New Sums of Three Cubes (Math. Comp. Vol. 78, no. 266: pp. 1227 – 1230)