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**ABSTRACT:**In this paper, we shall prove that for a sufficiently large odd numberN, the equation $$N = p_1 + p_2 + p_3 ,\frac{N}{3} - N^{\tfrac{7}{{12}} + e}< p_i \leqslant \frac{N}{3} + N^{\tfrac{7}{{12}} + e} (i = 1,2,3)$$ has solutions.Acta Mathematica Sinica 01/1994; 10(4):369-387. · 0.48 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**1. We prove that there is a set of nonnegative integers A, with counting function A(x) = #(A " [110/1996; -
##### Chapter: The Probabilistic Method

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