2.In this paper, the relation among the polynomial in several elements and the periodand linear complexity of the clock controlled sequences over the finite field GF(q)(q=p~a, p≥2 is a prime number, a≥1 is a positive integernumber)is discussed.
5.A positive integer n is called a tau number ifτ(n)|n, whereτis the divisor function. Let T(x) denote the number of tau numbers not exceeding x, Kennedy and Cooper have showed that T(x)=o(x). This paper gives an improvement of this result.
8.Where R_I(m,n) is the first Cartan domain in the sense of Loo-Keng HUA, det indicates the determinate, Z indicates the conjugate and transpose of Z, r,m, and n are positive integer numbers, K is a positive real number.
9.In this paper,the author has proved that the Diophantine y(y+1)(y+2)(y+3)=nx(x+1)(x+2)(x+3) has no integer solutions when n=13~(2k),k is a natural number .