丢番图方程(8a^3-3a)~x+(3a^2-1)~y=(4a^2-1)~z的正整数解

The positive integer solution of Diophantine equations (8a^3-3a)~x+ (3a^2-1)~y=(4a^2-1)~z

设a是大于3的正整数.作者应用Jacobi符号的性质和(两个)代数数对数线性型的下界估计,证明了指数丢番图方程(8a^3-3a)~x+(3a^2-1)~y=(4a^2-1)~z仅有正整数解(x,y,z)=(2,1,3).

Let n 〉3 be positive integer. In this paper, by the qualities of Jacobi symbol and lower bounds for linear forms in the logarithms of （two） algebraic numbers, the atuthors proved that the Diophantine equation （8a3-3a）^x＋（3a2-1）y=（4a2-1）^zhas only positive integer solution （x,y,z） = （2,1,3）.