Abstract
We prove that, with at most \(O(N^{\frac{17}{192}+\varepsilon})\) exceptions, all even positive integers up to N are expressible in the form p 21 + p 22 + p 33 + p 34 + p 45 + p 46 , where p1, p2, …, p6 are prime numbers. This gives large improvement of a recent result \(O(N^{\frac{13}{16}+\varepsilon})\) due to M. Zhang and J. J. Li.
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Acknowledgements
The author would like to express the most sincere gratitude to Prof. Zhixin Liu for his valuable advice and constant encouragement. This work was supported by the National Natural Science Foundation of China (Grant No. 11871367).
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Zhang, R. Slim exceptional set for sums of two squares, two cubes, and two biquadrates of primes. Front. Math. China 14, 1017–1035 (2019). https://doi.org/10.1007/s11464-019-0794-4
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DOI: https://doi.org/10.1007/s11464-019-0794-4