Abstract
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.
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