Magic Series

$n$ numbers form a magic series of degree $p$ if the sum of their $k$th Powers is the Magic Constant of degree $k$ for all $k\in [1,p]$.

See also Magic Constant, Magic Square

References

Kraitchik, M. ``Magic Series.'' §7.13.3 in Mathematical Recreations. New York: W. W. Norton, pp. 183-186, 1942.