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  • 1 Department of Mathematics, Tongji University, Shanghai 200092, P.R. China
  • | 2 Department of Mathematics, Shanghai University, Shanghai 200436, P.R. China
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Let Pr denote an almost-prime with at most r prime factors, counted according to multiplicity, and let E3(N) denote the number of natural numbers not exceeding N that are congruent to 4 modulo 24 yet cannot be represented as the sum of three squares of primes and the square of one P5. Then we have E3(N)≪log1053N. This result constitutes an improvement upon that of D. I. Tolev, who obtained the same bound, but with P11 in place of P5.

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