设P为充分大的正整数,矩阵(aij)n×(2n+1)的所有n级子式全不为0,且在这些n级子式间没有1以外的公因子,b1,…,6n为n个整数,U=P2/3log^6n+660P.则素数变数的线性方程组^2n+1∑v=1auvPv=6u(u=1,…,n)在小区间P〈Pv≤P+U(v=1,…,2n+1)上有素数解,并给出了其素数解的个数的渐近公式.
Suppose that P is a sufficiently large positive integer. All the n-th subdeterminant of the matrix (aij ) n × (2n + 1) are non-zero and random two of them are pairwise prime, b 1,…, bn are given integers.U=P2/3log^6n+660P . Then the system of linear equations of prime variables ∑v=1^2n+1auvPv = bu (u = 1,…, n) exists solutions in short interval P〈 pv≤P + U(v=1,… ,2n + 1). An asymptotic formula of the number of its prime solutions is given.