1.Let n ≥ 2 be a given integer. Let k ≥ 2 be an arbitrary given integer. Let F be a field of characterstic 2 and M_n(F) be the set of all n x n matrices on F and T_n(F) be the set of all n x n upper triangular matrices on F.
4.Proposition B For every pair (n, d) of positive integers, there exists a positive integer f (n, d) suth that: For every prime P>f (n, d) and every field K of characteristic P, if a polynomial mapping F:K~n→K~n satisfies deg F≤d and detJ(F)=1, then F is invertible.
5.Let a>3 be an integer,the author applies a deep theorem of Bilu,Hanrot and Voutier and some results on the class number of quadratic field to show that the only positive integer solution of the diophantine equation(8a3-3a)2x+(3a2-1)y=(4a2-1)z is(x,y,z)=(1,1,3).
6.A method of C-implementing the perations on a finite field whose radix is a power of prime integer was given by means of shifting division for polynomials, and some main C-functions requred by implementing the operations were listed.
7.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 integer number)is discussed.
8.Let α_1,…,α_n be a K-dimensional set of vectors over the infinite field F (K is a positive integer,greater than 2). If there is C_i∈F,none of which is zero,so that sum from i=1 to n C_iα_i=0,then α_1,α_2,…,α_n is a t-linear depen- dent set of vectors.
设 a_1,…a_n 是无限域 F 上的 k (k 为正整数,且 k≥2)维向量组,若存在全不为零的 C_i∈F,使得 sum from i=1 to n Ci_a_i=0,则 a_1,a_2…,a_n 是 t—线性相关的向量组。收藏指正
