Problem #389: Is it true that for every $n\geq 1$ there is a $k$ such...

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Progress

Asked by Erdős and Straus.
For example when $n=2$ we have $k=5$:\[2\times 3 \times 4 \times 5\times 6 \mid 7 \times 8 \times 9\times 10\times 11.\]and when $n=3$ we have $k=4$:\[3\times 4\times 5\times 6 \mid 7\times 8\times 9\times 10.\]Bhavik Mehta has computed the minimal such $k$ for $1\leq n\leq 18$ (now available as A375071 on the OEIS).