Erdős problem 677

Denote by $M(n, k)$ the least common multiple of the finite set $\{n+1, \dotsc, n+k\}$ . Is it true that for all $m \geq n + k$ , we get $M(m, k) \neq M(n, k)$ ?

Sources

The source's own material, retained exactly.

2 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

677.lean

Retained formal statement2 of 2

Erdős expected very few solutions for $M(n, k) = M(m, l)$ , where $m \geq n + k$ and $l > 1$ . The only solutions he knew were the following.

FormalConjectures/ErdosProblems/677.leanErdos677.lcmInterval_eq_example11 lineExact file

1Finset.lcmInterval 4 3 = Finset.lcmInterval 13 2 ∧ Finset.lcmInterval 3 4 = Finset.lcmInterval 19 2

TestStatement only, no proof