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1

You could also use IntegerPartitions, which is faster than PowersRepresentations. Select[IntegerPartitions[10400, {7}, Range[101]^2], DuplicateFreeQ[#]&] or Pick[#, Map[DuplicateFreeQ, #]]&[IntegerPartitions[10400, {7}, Range[101]^2]] The maximum of the range, 101, is approximately the square root of the input integer 10400.


2

Select[PowersRepresentations[10400, 7, 2], DuplicateFreeQ[#] && ! MemberQ[#, 0] &]


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