In this paper we show how the quantitative forms of Kronecker's theorem in Diophantine approximations can be applied to investigate viewobstruction problems. In particular we answer a question in [Yong-Gao Chen, On a conjecture in Diophantine approximation, III, J. Number Theory 39 (1991),
Abstract. Let A be an infinite set of natural numbers. For n ∈ N, let r(A, n) denote the number of solutions of the equation n = a + b with a, b ∈ A, a ≤ b. Let |A(x)| be the number of integers in A which are less than or equal to x. In this paper, we prove that, if r(A, n) = 1 for all sufficiently large integers n, then(log x/ log log x) 2 for all sufficiently large x.
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