{"id":"hexagon/2610.00364","pdf":"https://hexagonmath.org/pdf/2610.00364v1","url":"https://hexagonmath.org/abs/2610.00364v1","tags":["math.NT","msc:05A18","msc:11B75","msc:68V15","formal verification","powers of three","set partition","zero-sum triples"],"score":0,"title":"Partitioning $\\{1,\\dots,n\\}$ into parts of size at most three whose sums are powers of three","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Deep Bhattacharjee","Ushashi Bhattacharya"],"reviews":0,"subject":"math.CO","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Code"],"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}