Abstract
It is widely conjectured that every sufficiently large integer satisfying certain necessary congruence conditions is the sum of 4 cubes of prime numbers. As an approximation to this conjecture, we shall establish two results in this paper. Firstly, we show that every large odd integer is the sum of a prime, 4 cubes of primes and 15 powers of 2. Secondly, we show that the conjecture is true for at least \(8.25\%\) of the positive integers.
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Ching, T.W., Tsang, K.M. Waring–Goldbach problem involving cubes of primes. Math. Z. 297, 1105–1117 (2021). https://doi.org/10.1007/s00209-020-02550-4
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DOI: https://doi.org/10.1007/s00209-020-02550-4