On the Additive Completion of Polynomial Sets Original Research Article

Let P be a polynomial of degree k ≥ 2 with nonnegative coefficients. Let B be a set of nonnegative numbers such that every integer n ≤ N can be written as n = b + P(λ) for some integer λ and some b in B. Then, given a positive real number ε, we show that B P−1(N) > ((1 − 1/k)−1 sin(π/k)/(π/k) − ε)N for sufficiently large N.