Abstract
Let 1 < c < 15/14 and N a sufficiently large real number. In this paper we prove that, for all η ∈ (N, 2N\ A with \(\left| A \right| = O\left( {N exp\left( { - \frac{1}{3}\left( {\frac{L}{c}} \right)^{1/5} } \right)} \right)\), the inequality \(\left| {p_1 ^c + p_2 ^c - \eta } \right| < \eta ^{1 - \frac{{15}}{{14c}}} L^8 \) has solutions in primes \(p_1 ,p_2 \underline{\underline < } N^{\frac{1}{c}} \).
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Laporta, M.B.S. On a Binary Diophantine Inequality Involving Prime Numbers. Acta Mathematica Hungarica 83, 179–187 (1999). https://doi.org/10.1023/A:1006763805240
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DOI: https://doi.org/10.1023/A:1006763805240