What is the conjecture

https://www.erdosproblems.com/951

Let $1<a_1<\cdots$ be a sequence of real numbers such that
$$\left\lvert \prod_i a_i^{k_i}-\prod_j a_j^{\ell_j}\right\rvert \geq 1$$
for every distinct pair of non-negative finitely supported integer tuples $k_i,\ell_j\geq 0$. Is it true that
$$\#\{ a_i \leq x\} \leq \pi(x)?$$

Status: open

Choose either option

• I plan on working on this conjecture
• This issue is up for grabs: I would like to see this conjecture added by somebody else