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Erdős problem 728

Whether there are infinitely many integers a,b,na, b, n with a,b≥εna, b \ge \varepsilon n such that a!⋅b!a!\cdot b! divides n!⋅(a+b−n)!n!\cdot(a+b-n)! while a+ba+b exceeds nn by more than C⋅log⁡nC\cdot\log n.

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Whether there are infinitely many integers $a, b, n$ with $a, b \ge \varepsilon n$ such that $a!\cdot b!$ divides $n!\cdot(a+b-n)!$ while $a+b$ exceeds $n$ by more than $C\cdot\log n$.

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