2.A method of C-implementing the perations on a finite field whose radix is a power of primeinteger was given by means of shifting division for polynomials, and some main C-functions requred by implementing the operations were listed.
4.Suppose G contains no sections isonaorphic to the extension qPn: (Zm,Zp) of an elementary abelian q-group of order qpn by the group Zm:Zp for any prime number q and any integer n with m= (qpn-1)/(qn-1).
5.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.
6.Let r be an odd integer with r > 1, m be an even integer. Let Ur, Vr beintegers satisfying and c was a power of prime, then the equation ax + by = cz had only the positive integer solution (x,y,z) = (2, 2,r).
7.5(mod8), c is a power of a prime and the equationax+by=cz has a positive integer solution (x, y, z) = (2,2, r), where r is an odd integer with r>1, then the exceptional solutions (x, y, z) of the equation satisfy x=2 and y=z=1(mod 2).
10.We prove that if a+b2l-1=c2,b ≡ 5(mod 12) and c is an odd prime with c≡-1(mod b2l),where l is a positive integer,then the equation ax+by=cz has only the positive integer solution(x,y,z)=(1,2l-1,2).
本文证明了:当a+b2 l-1=c2,b≡5(m od 12),c是适合c≡-1(m od b2 l)的奇素数,其中l是正整数时,方程ax+by=cz仅有正整数解(x,y,z)=(1,2 l-1,2).收藏指正
