erdos_123.variants.powers_2_3

A simpler case: the set of numbers of the form $2^k 3^l$ ($k, l ≥ 0$) is d-complete. This was initially conjectured by Erdős in 1992, who called it a "nice and difficult" problem, but it was quickly proven by Jansen and others using a simple inductive argument: - If $n = 2m$ is even, apply the inductive hypothesis to $m$ and double all summands. - If $n$ is odd, let $3^k$ be the largest power of $3$ with $3^k ≤ n$, and apply the inductive hypothesis to $n - 3^k$ (which is even). Reference: [Er92b] Erdős, Paul, _Some of my favourite problems in various branches of combinatorics_. Matematiche (Catania) (1992), 231-240.

theorem erdos_123.variants.powers_2_3 : IsDComplete (↑(powers 2) * ↑(powers 3))

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