Finding Certain Arithmetic Progressions in 2-Coloured Cyclic Groups

We say a pair of integers (a, b) is findable if the following true. For any δ > 0 there exists p0 such that for prime p ≥ and red-blue colouring ℤ/pℤ in which each colour has density at least δ, we can find an arithmetic progression length + b inside whose first elements are red last blue. Szemeredi’s Theorem on progressions implies (0, k) (1, find-able k. prove (2, also However, same not true (3, k). Indeed, give construction showing (3,30000) findable. show (14, 14)