Tarry-Escott Problem
For each Positive Integer 
, there exists a Positive Integer 
and a Partition of 
,..., 
as a disjoint union of two sets 
and 
, such that for 
,
The results extended to three or more sets of Integers are called Prouhet's Problem.See also Prouhet's Problem
References
Dickson, L. E. History of the Theory of Numbers, Vol. 2: Diophantine Analysis. New York: Chelsea, pp. 709-710, 1971. Hahn, L. ``The Tarry-Escott Problem.'' Problem 10284. Amer. Math. Monthly 102, 843-844, 1995.
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