Abstract
Let P i , 1 ≤ i ≤ 5, be prime numbers. It is proved that every integer N that satisfies N ≡ 5(mod24) can be written as \( N = p^{2}_{1} + p^{2}_{2} + p^{2}_{3} + p^{2}_{4} + p^{2}_{5} ,{\text{where}}{\left| {{\sqrt N }5 - p_{i} } \right|} \leqslant N^{{\frac{1} {2} - \frac{{19}} {{850}} + \in }} \).
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Bauer, C. Sums of Five Almost Equal Prime Squares. Acta Math Sinica 21, 833–840 (2005). https://doi.org/10.1007/s10114-004-0506-0
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DOI: https://doi.org/10.1007/s10114-004-0506-0