• Title, Summary, Keyword: Hardy-Littlewood method

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ON A WARING-GOLDBACH PROBLEM INVOLVING SQUARES, CUBES AND BIQUADRATES

  • Liu, Yuhui
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1659-1666
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    • 2018
  • Let $P_r$ denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper, it is proved that for every sufficiently large even integer N, the equation $$N=x^2+p_1^2+p_2^3+p_3^3+p_4^4+p_5^4$$ is solvable with x being an almost-prime $P_4$ and the other variables primes. This result constitutes an improvement upon that of $L{\ddot{u}}$ [7].