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Number of ways of splitting the numbers from 1 to 16 into two groups so that the numbers in each group have the same sum of n-th powers.
2

%I #7 Apr 19 2013 08:58:31

%S 657,57,1,1

%N Number of ways of splitting the numbers from 1 to 16 into two groups so that the numbers in each group have the same sum of n-th powers.

%C For n=1,2 there are numerous ways, while for each of n=3 and n=4 there is only one way: n=3:{1,4,6,7,10,11,13,16},{2,3,5,8,9,12,14,15} (see A133483-A133484), n=4: {1,2,3,4,8,9,10,11,12,16},{5,6,7,13,14,15}.

%C Presumably for n >= 4 there are no solutions.

%Y Cf. A133483, A133484, A135419.

%K nonn

%O 1,1

%A _Zak Seidov_, Dec 01 2007