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关于指数Diophantine方程ax+dby=czOACSTPCD

On the exponential Diophantine equation ax+dby=cz

中文摘要英文摘要

设a,b,c,d,l,m,n是给定的适合al+dbm=cn,gcd (a,db)=1,l>1,m>1,n>1的正整数.本文中证明了:如果a≡3(mod 8),2‖b,c是素数方幂,(b/a)=-1,(d/a)=1,l=m=2,则方程ax+dby=cz仅有正整数解(x,y,z)=(2,2,n)适合min(x,y,z)>1.

Let a,b,c,d,l,m,n be fixed positive integers satisfying al+dbm=cn,gcd(a,db)=1,l>1,m>1 and n>1.It was prove that if a≡3(mod8),2‖b,c is a prime power,(b/a)=-1,(d/a)=1 and l=m=2,then the equation ax+dby=cz has only one positive integer solution (x,y,z)=(2,2,n) satisfying x>1,y>1 and z>1.

乐茂华

湛江师范学院,数学系,广东,湛江,524048

数理科学

指数Diophantine 方程正整数解完全确定

exponential Diophantine equationpositive integer solutioncomplete deterimination

《纺织高校基础科学学报》 2003 (2)

99-101,3

The National Natural Science Foundation of China(No.10271104),the Guangdong Provincial Natural Science Foundation(No.011871) and the Natural Science Foundation of the Education Departement of Guangdong Province(No.0161).

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