Write $M(n, k)$ be the least common multiple of $\{n+1, \dotsc, n+k\}$.
Let $k$ be sufficiently large. Are there infinitely many $m, n$ with $m \geq n + k$ such that
$$
M(n, k) > M(m, k + 1)
$$?
The answer is yes, as proved in a strong form by Cambie [Ca24].
[Ca24] S. Cambie, Resolution of an Erdős' problem on least common multiples. arXiv:2410.09138 (2024).
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