摘要
本文通过计算Jacobi符号,运用代数数的对数线性型的下界估计,证明了:当整数a>1时,指数丢番图方程a^x+(3a^2-1)~y=(4a^2-1)~z仅有正整数解(x,y,z)=(2,1,1).
In this paper,we use properties of the Jacobi symbol and lower bounds for linear forms in two logarithms of algebraic numbers to prove that the diophantine equation ax ＋（3a2-1）y =（4a2-1）z has only the positive integer solution（x,y,z） =（2,1,1） for the integer a1.
出处
《数学进展》
CSCD
北大核心
2011年第2期227-234,共8页
Advances in Mathematics（China）
基金
supported by the Applied Basic Research Foundation of Sichuan Provincial Science and Technology Department(No.2009JY0091).
关键词
指数丢番图方程
JACOBI符号
对数线性型
exponential diophantine equations
Jacobi symbols
linear forms in the logarithms
