... that x < kx − , and for each y ∈ (0, x] , not both y and kx − y can k be in S Because of this “forbidden pairing with respect to x of (0, x] with [kx − x, kx), and since < kx − x < kx < 1, k Now ... Because of these “forbidden pairs with respect to x, ” µ (S ∩ [kx − 1, 1]) ≤ [1 − (kx − 1)] (3.1) If we now let S = w|w ∈ S ∩ (0, kx − 1] kx − then S is k-sum-free and µ(S ∩ (0, kx − 1] kx − 1 = (µ(S) ... k2 g(m, y) = (k2 − 2) h(m, y) = m−1 k2 − 2y m−1 − 1 f (m, y) g(m, y) k With y fixed, the function Fy (m) = f(m, y) is an increasing linear function of m with root m (y) given by where m...