The exponential Diophantine equation $(3am^2-1)^x+(a(a-3)m^2+1)^y=(am)^z$

Authors : Nai-juan DENG, Dan-yao WU, Ping-zhi YUAN

Pages : 2561-2567

View : 8 | Download : 8

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let $a,\ m$ be positive integers such that $am\not\equiv0\pmod{3}, 2\nmid a$, and $a>3$. We prove that the exponential Diophantine equation $insert ignore into journalissuearticles values(3am^2-1);^x+insert ignore into journalissuearticles values(ainsert ignore into journalissuearticles values(a-3);m^2+1);^y=insert ignore into journalissuearticles values(am);^z$ has only the positive integer solution $insert ignore into journalissuearticles values(x,y,z);=insert ignore into journalissuearticles values(1,1,2);$.
Keywords : Diophantine equation, positive integer solution, Fibonacci number