On Exceptional Sets for Waring-Goldbach Problems with Unlike Powers

• DOI: 10.1007/s11464-024-0052-2
• Publication Date: 2025-01-04T05:08:30Z
• Authors: Rui Zhang; Wei Zhang
• Keywords: Goldbach's conjecture; Representation; Natural number; Residue (chemistry)

Estimates are obtained for the number of natural numbers n in certain residue classes that do not have a representation form $$n = {p_1} + p_2^2 p_3^k,$$ k 3 or 4 respectively, where pi primes. We improve previous results [Monatsh. Math., 2019, 188(2): 269–285].