Let $1 \leq a_{1} < \dots < a_{k} \leq x$ . How many of the partial products $a_{1}, a_{1} a_{2}, \dots, a_{1} \dots a_{k}$ can be squares? Is it true that, for any $ϵ > 0$ , there can be more than $x^{1 - ϵ}$ squares?

Worked, still open.

number theory · solved · possible · 0 attempts

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