关于指数Diophantine方程ax+dby=czOACSTPCD
On the exponential Diophantine equation ax+dby=cz
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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