On sums of a prime and four prime squares in short intervals

In this paper, we are able to sharpen Hua's classical result by showing that each sufficiently large integer N≢1(mod3) can be written asN=p+p12+p22+p32+p42,with |p−N5|⩽N5U,|pj−N5|⩽U,j=1,2,3,4, where U=N41100+ε and p  , pjpj are primes. This result improves a previous result with U=N41100+ε replaced by U=N511+ε.