Abstract:
We prove an asymptotic formula for the number of representations of a sufficiently large natural number $N$ as the sum of two primes $p_1$ and $p_2$ and the cube of a natural number $m$ satisfying the conditions $|p_i-N/3|\le H$, $|m^3-N/3|\le H$, $H\ge N^{5/6}\mathscr L^{10}$.
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