Let $a,b,c\ge 1$ be three integers which are pairwise coprime. Is every large integer the sum of distinct integers of the form $a^k{b}^l{c}^m$ ($k,l,m\ge 0$), none of which divide any other?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

This is **not known in general** (for the interesting case where (a,b,c\ge 2)). It is a well-known open problem of Erdős, usually stated in terms of **(d)-complete** sets/sequences. ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.