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≡ 7 8, n≡ 1 3, n≡ 0,2,3 5 , can be represented as 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 ].