摘要
It is proved that every large integerN≡5 (mod 24) can be written as $N = p_1^2 + ... + p_5^2 $ with each primep j satisfying $|p_j - \sqrt {N/5} | \leqslant N^{\frac{{12}}{{25}} + E} $ , which gives a short interval version of a classical theorem of Hua.
It is proved that every large integer N≡5 (mod 24) can be written as N=p 2 1+...+p 2 5 with each prime p j satisfying |p j-N/5|≤N 1225+ε , which gives a short interval version of a classical theorem of Hua.
基金
ProjectsupportedbytheTransCenturyTrainingProgrammeFoundationfortheTalentsbytheStateEducationCommissionandtheNationalNaturalScienceFoundationofChina (GrantNo .1970 10 19)
