In this paper, we prove that each sufficiently large integer N ≠1（mod 3） can be written as N=p＋p1^2＋p2^2＋p3^2＋p4^2, with｜p-N/5｜≤U,｜pj-√N/5｜≤U,j=1,2,3,4,where U=N^2/20＋c and p,pj are primes.
In this paper we prove that, with at most O（N^5/12＋ε） exceptions, all positive odd integers n ≤ N with n ≡ 0 or 1（mod 3） can be written as a sum of a prime and two squares of primes.
基金the National Natural Science Foundation of China (Grant No.10701048)
文摘In this paper, we prove that each sufficiently large integer N ≠1（mod 3） can be written as N=p＋p1^2＋p2^2＋p3^2＋p4^2, with｜p-N/5｜≤U,｜pj-√N/5｜≤U,j=1,2,3,4,where U=N^2/20＋c and p,pj are primes.
基金Project supported by National Natural Science Foundation(No. 90304009)Foundation of Qufu Normal University for Ph.D.
文摘In this paper we prove that, with at most O（N^5/12＋ε） exceptions, all positive odd integers n ≤ N with n ≡ 0 or 1（mod 3） can be written as a sum of a prime and two squares of primes.
