Sums of Numbers with Small Partial Quotients II Original Research Article

For mset membership, variantimage+ let F(m) be the set of numbers with an infinite continued fraction expansion where all partial quotients, except possibly the first, do not exceed m. In 1975, James Hlavka conjectured that F(6)+F(2)≠image. We shall disprove Hlavkaʹs conjecture, showing that in fact F(5)±F(2)=image.