摘要
本文用G.D.Birkhff和H.S.Vandiver关于本原因于的一些结果,讨论了比A.Rotkiewicz问题更一般的伪素数同余式a^(cn-k)b^(mond n) (*)其中0<b<a,(a,b)=1,c<0,k均为整数,主要结果如下:定理,除(i)a-b=2,(c,k)=(2,3)或(3,5),(ii)a-b=1,|c-k|=1和(iii)c=1,k=3,a^2-b^2=2~m。或c=1,k=2,a-b=1或3或c=1,k=0,a-b=1之外,均有无穷多个正整数n适合同余式(*)。其次,本文回答了Stanley J.Benkoski在M.R.(87e:11006)中提的一个问题,还给出如下猜想。猜想:由任意给定的正整数a、b、c、k除(a,b,c,k)=(1+b,b,1,0)之外,均有无穷多个正整数n满足同余式(*)
In this paper,using some results on primitive prime factors achieved by G.D.Birkhoff and H.S.Vandiver,we discuss a problem on Pseudoprime Congruences which is more generalized than A Rothkiewicz Problem a~≡b^((modn)(*) where 0<b<a,(ab)=1,c<0,k be integers The main results is as as follows: Theorem,Apart from(i)a-b=2 and(c,k)=(2,3)or(3,5).(ii)a-b= 1,|c-k|=1 and(iii)c=a,k=3,a^2-b^2=2~mor c=1,k=2,a-b=1 or 3 or c=1,k=0,a-b=1,there are infinitely many positive integers n satisfy the Congruence(*) Next,the paper gives an answer to a problem raised by stanley J Benkoski in Mathematical Reviews(87e:11006)and offersthe following conjecture. Conjecture:For any positive integers a,b,c,k other than(1+b,b 1,0),there are infintely many positive integers satisfy(*)
出处
《长沙铁道学院学报》
CSCD
1991年第1期87-94,共8页
Journal of Changsha Railway University
关键词
伪素数同余式
本原素因子
本原因子
pseudoprime congruence
primitive prime factor
rpimitive faccor
primitive prime power factor
primitive factor
