Last cases of Dejean’s conjecture

Dejean conjectured that the repetition threshold for a k-letter alphabet is when k≥5. Dejean’s conjecture has already been proved for k≤14 and for k≥27. We present here a proof for 8≤k≤38. The same technique is also applied to prove Ochem’s stronger version of the conjecture for 9≤k≤38.