Conjecture: Let $n$ $∈$ $N$. Then for each factor $m ≥ n$ of $n$($n + 1$)/$2$, one can partition the set $\{1, 2, 3, \ldots , n\}$ into disjoint subsets such that the sum of elements in each subset is equal to $m$.

The conjecture is based on numerical evidence.


closed as off-topic by Parcly Taxel, iadvd, suomynonA, SchrodingersCat, Tad Oct 16 '16 at 2:30

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  • $\begingroup$ This is an interesting question! You write 'prove that...' not 'is it true that...?' or 'prove or give a counterexample...'. What makes you so sure that it is true? Did you compute lots of examples? $\endgroup$ – Vincent Oct 11 '16 at 10:44
  • $\begingroup$ Yeah i did compute some examples and i made this conjecture. $\endgroup$ – dark_night_returns Oct 11 '16 at 11:01
  • $\begingroup$ Anyone who can settle this ??? $\endgroup$ – dark_night_returns Oct 11 '16 at 12:04
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    $\begingroup$ I’ve edited the question to make it clear that this is a conjecture, in hopes of forestalling a fifth vote to close it. $\endgroup$ – Brian M. Scott Oct 13 '16 at 7:07
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    $\begingroup$ Possible duplicate of Partition of ${1, 2, ... , n}$ into subsets with equal sums. $\endgroup$ – Tad Oct 16 '16 at 2:30