On a Version of the Hua Problem

A. Kirkoryan, D. I. Tolev

Sofia University St. Kliment Ohridski

Abstract: 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.

UDC: 511.333

Received: 24.11.2009

DOI: 10.4213/mzm8813

 English version: Mathematical Notes, 2010, 88:3, 365–373

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