Permanent problem IDPPL 043
Additive combinatorics
Let r_k(N) be the largest possible size of a subset of {1,…,N} that does not contain any non-trivial k-term arithmetic progression. Prove an asymptotic formula for r_k(N).
Let r_k(N) be the largest possible size of a subset of {1,…,N} that does not contain any non-trivial k-term arithmetic progression. Prove an asymptotic formula for r_k(N).
A solution must appear in a reputable journal, with documentation that Erdős offered the displayed amount. Claims are administered by the Combinatorics Foundation; erdosproblems.com does not pay awards.