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Is it true that for every $n$ there is a $k$ such that \[\prod_{1\leq i\leq k}(n+i) \mid \prod_{1\leq i\leq k}(n+k+i)?\]
Asked by Erdős and Straus. For example when $n=2$ we have $k=4$: \[3\cdot 4\cdot 5\cdot 6 \mid 7\cdot 8\cdot 9\cdot 10.\] No example was known for $n\geq 10$.