Is there some function $f (r)$ such that $f (r) \to \infty$ as $r \to \infty$ , such that, for infinitely many $n$ , there exist $a_{1}, a_{2}$ with $a_{1} + a_{2} > n + f (r) lo g n$ such that $a_{1}! a_{2}! ∣ n! 2^{n} 3^{n} \dots p_{r}^{n}$ ?

Worked, still open.

number theory · solved · 0 attempts

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