On a version of the Hua problem
The authors prove that almost all natural numbers satisfying necessary congruence conditions can be written as the sum of three squares of primes, at least one of which is of the form \(1+x^2+y^2\). The proof is an adaption of the second author's work [see Acta Arith. 142, No. 2, 169--178 (2010; Zbl 1213.11174) and J. Number Theory 130, No. 2, 439--457 (2010; Zbl 1230.11128)] on similar variants of the Goldbach problem.
scientific article; zbMATH DE number 5980679
scientific article