Combinatorics at GCSE and A-level: "For which values of positive integer k is it..."

Michael G.

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Combinatorics at GCSE and A-level: "For which values of positive integer k is it..."

I'm on a GCSE-A level syllabus currently, and I can't seem to think of any algebraic equation that I could comprise to solve this (with the GCSE/early a level syllabus). The question in full is
For which values of positive integer k is it possible to divide the first 3k positive integers into three groups with the same sum? (e.g. if k = 3, then the first 3k integers are 1,2,3,4,5,6,7,8,9. You can split these into 3 groups of 15, for example {{1,2,3,4,5},{7,8},{6,9}}. so it is possible for k=3)
Any help would be appreciated. Thanks
 
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