On Waring–Goldbach problem for two squares and five biquadrates

In this paper, it is proved that every sufficiently large positive integer n, which satisfies $$ n\equiv 7\!\!\pmod 8, n\equiv 1\!\!\pmod 3, n\equiv 0,2,3\!\!\pmod 5$$ n ≡ 7 ( mod 8 ) , n ≡ 1 ( mod 3 ) , n ≡ 0 , 2 , 3 ( mod 5 ) , can be represented as $$\begin{aligned} n=p_1^2+p_2^2+p_3^4+p_4^4+p_5^4+p_6^4+p_7^4. \end{aligned}$$ n = p 1 2 + p 2 2 + p 3 4 + p 4 4 + p 5 4 + p 6 4 + p 7 4 . This result gives a large improvement upon the previous results of Cai [1] and Hooley [3].