Erdős problem 678 · problems.science

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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7 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

678.lean

Retained formal statement5 of 7

The referee of [Er79] found the example $M(132, 7) > M(139, 8)$ , showing that there are cases where $M(n, k) > M(m, k + 1)$ with $m \geq n + k$ . [Er79] Erdős, Paul, Some unconventional problems in number theory. Math. Mag. (1979), 67-70.

FormalConjectures/ErdosProblems/678.leanErdos678.lcmInterval_lt_example21 lineExact file

1Finset.lcmInterval 139 8 < Finset.lcmInterval 132 7

TestStatement only, no proof

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