HUA’S THEOREM WITH FIVE ALMOST EQUAL PRIME VARIABLES

It is proved that each sufficiently large integer N=5(mod24) can be written as N=p1^2+p2^2+p3^2+p4^2+p5^2 with|pj=√N/5|±、≤U=N^1/2-1/35+e,where pj ae primes.This result,which is obtained by an iterative method and a hybrid estimate for Dirichlet polynomial, improves the previous results in this direction.