Geodesic
On a Version of the Hua Problem
Matematičeskie zametki, Tome 88 (2010) no. 3, pp. 405-414

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We prove that almost all natural numbers $n$ satisfying the congruence $n\equiv3\pmod{24}$, $n\not\equiv0\pmod5$, can be expressed as the sum of three squares of primes, at least one of which can be written as $1+x^2+y^2$.
Keywords: prime number, Hua problem, natural number, multiplicative function, Euler function, Cauchy inequality, Dirichlet $L$-series. 
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     author = {A. Kirkoryan and D. I. Tolev},
     title = {On a {Version} of the {Hua} {Problem}},
     journal = {Matemati\v{c}eskie zametki},
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     language = {ru},
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A. Kirkoryan; D. I. Tolev. On a Version of the Hua Problem. Matematičeskie zametki, Tome 88 (2010) no. 3, pp. 405-414. http://geodesic.mathdoc.fr/item/MZM_2010_88_3_a8/