Abstract
We prove that almost all positive even integers n can be represented as p 22 + p 33 + p 44 + p 55 with \(\left| {p_k^k - {1 \over 4}N} \right| \leqslant {N^{1 - 1/54 + \varepsilon }}\) for 2 ⩽ k ⩽ 5. As a consequence, we show that each sufficiently large odd integer N can be written as p1 + p 22 + p 33 + p 44 + p 55 with \(\left| {p_k^k - {1 \over 5}N} \right| \leqslant {N^{1 - 1/54 + \varepsilon }}\) for 1 ⩽ k ⩽ 5.
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The research has been supported by NSFC (11871307).
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Zhang, Q. On an additive problem of unlike powers in short intervals. Czech Math J 72, 1167–1174 (2022). https://doi.org/10.21136/CMJ.2022.0417-21
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DOI: https://doi.org/10.21136/CMJ.2022.0417-21