Permanent problem IDPPL 076
Number theory
Let f(n,m) be minimal such that in (m,m+f(n,m)) there exist distinct integers a_1,…,a_n such that k∣ a_k for all 1≤ k≤ n. Prove that \max_m f(n,m) ≤ n^(1+o(1)) and that \max_m (f(n,m)-f(n,n))→ ∈fty.
Let f(n,m) be minimal such that in (m,m+f(n,m)) there exist distinct integers a_1,…,a_n such that k∣ a_k for all 1≤ k≤ n. Prove that \max_m f(n,m) ≤ n^(1+o(1)) and that \max_m (f(n,m)-f(n,n))→ ∈fty.
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