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Erdős problem 678

Write M(n,k)M(n, k) be the least common multiple of {n+1,…,n+k}\{n+1, \dotsc, n+k\}. Let kk be sufficiently large. Are there infinitely many m,nm, n with m≥n+km \geq n + k such that M(n,k)>M(m,k+1) 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 statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

678.lean

Retained formal statement7 of 7

Cambie [Ca24] found the example M(36,8)>M(48,9)M(36, 8) > M(48, 9). [Ca24] S. Cambie, Resolution of an Erdős' problem on least common multiples. arXiv:2410.09138 (2024).

FormalConjectures/ErdosProblems/678.leanErdos678.lcmInterval_lt_example41 lineExact file
Finset.lcmInterval 47 9 < Finset.lcmInterval 36 8
TestStatement only, no proof