1) prime polar divisor
素极除子
2) polar divisor
极除子
3) prime null divisor
素零除子
4) very ample divisor
极丰富除子
5) primitive divisor
本原素除子
1.
By applying the deep theorem of Bilu,Hanrot and Voutier about the existence of primitive divisors of Lucas numbers,we prove that the exponential diophantine equation x2+3m=yn has only positive integer solution(x,y,m,n)=(46,13,4,3) with n>2 and gcd=(x,y)=1.
利用Bilu,Hanrot和Voutier关于Lucas数本原素除子存在性的深刻结果,证明了指数丢番图方程x2+3m=yn仅有正整数解(x,y,m,n)=(46,13,4,3)适合n>2且gcd(x,y)=1。
2.
This thesis is to study the integer solutions and the number of theinteger solutions of some exponential diophantine equations by applyingthe deep theorem of Bilu, Hanrot and Voutier about the existence ofprimitive divisors of Lucas and Lehmer numbers, some fine results on therepresentation of the solutions of quadratic Diophantine equations and theclass number of quadratic field.
Voutier关于Lucas数和Lehmer数的本原素除子的存在性的深刻理论、二次丢番图方程解的表示以及二次域类数等方面的精细结果研究一些指数丢番图方程的整数解和解数。
3.
We apply a deep result of Bilu,Hanrot and Voutier on primitive divisors to show that if the class number of quadratic field Q((-b)~(1/2))is a power of 2,then,the Diophantine equation x~2 + b~y=c~z has only the positive integes solution (x,y,z)=(a,2,5)with min(x,y,z)>1.
利用Bilu,Hanrot and Voutiers关于本原素除子的深刻结果证明了:如果二次数域Q((-b)~(1/2))的类数是2的方幂,则丢番图方程x~2+b~y=c~z仅有正整数解(z,y,z)=(a,2,5)适合min(x,y,z)>1。
6) Minimal prime subgroup
极小素子群
1.
On the basis of the previous research result,a structure N=a~⊥of minimal prime subgroups for some spe- cial classes of l-groups is establisned in this artcle.
在l-群的极小子群研究的基础上就某些特殊类的l-群建立了极小素子群的一种结构N=a~⊥。
补充资料：只除
1.犹除非。
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