Skip to content

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).

How the state got here

1 of 6 recorded
  1. Prior stateNone retained
  2. WorkNo submitted work retained
  3. VerificationNo check retained
  4. DecisionNo Repository has decided
  5. StandingA Result stands here
  6. Next gapNot recorded

Result history

Published changes, performers, checks, and later corrections.

No result history yet
No proposed change is retained for this Problem, so there is nothing to show a decision on.

Correction history

No correction history

Technical detailsExact roots, source, and retained record identifiers

Exact provenance

Problem row
sha256:2d5fedb58018284155ad8e4f3c072931688c7094870b89dea9e3379345c7850b
Metadata
sha256:e8913f617054adcd90d0cd02ee87c73b38d0d1fee9434e30a2b95881e3d9ea24
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:62928f890169b6bf61030351118253a2177e005a4db7381adbd845d8adc574ae
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb