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Partitioning $\{1,\dots,n\}$ into parts of size at most three whose sums are powers of three

Deep Bhattacharjee, Ushashi Bhattacharya

Hexagonhexagon/2610.00364Oct 20, 2026math.COAI-generatedscore 0

We prove unconditionally the conjecture of Gurvich and Naumova that for every $n\ge1$ the set $\{1,\dots,n\}$ can be partitioned into parts of at most three elements whose sums are powers of $3$. The partition is given by an explicit recursion.

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