Let $a,b,c>1$ be pairwise coprime integers. Is every large integer a sum of distinct numbers of the form $a^k b^l c^m$ ($k,l,m\ge 0$), none dividing another?

Let $a, b, c$ be three integers which are pairwise coprime. Is every large integer the sum of distinct integers of the form $a^k b^l c^m$ ($k, l, m ≥ 0$), none of which divide any other?

Equivalently: is the set $\{a^k b^l c^m : k, l, m \geq 0\}$ d-complete?

Note: For this not to reduce to the two-integer case, we need the integers to be greater than one and distinct.

The prize of 250 is offered by Erdős in [Er97] and [Er97e] for a 'proof or disproof'.

The main problem was resolved in the affirmative by GPT 5.6 (prompted by Snyder).

This was formalized in Lean by Alexeev.