Erdős Problem 437

Let $1\leq a_1<\cdots<a_k\leq x$. How many of the partial products $a_1,a_1a_2,\ldots,a_1\cdots a_k$ can be squares? Is it true that, for any $\epsilon>0$, there can be more than $x^{1-\epsilon}$ squares?

The answer is yes, which follows from work of Bui, Pratt, and Zaharescu [BPZ24], as noted by Tao [Ta24].