Abstract
For , with a fixed odd prime, and , the asymptotic formula is proved, where is the number of positive integer solutions of , is a polynomial of degree in with coefficients depending on and , with a positive constant depending on , and the constant involved in the order depends on , and . The proof relies on an idea of A. A. Karacuba that permits one to solve this problem by means of a scheme for a ternary additive problem. Bibliography: 10 titles.
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