The Exponential Diophantine Equation4m2+1x+5m2-1y=(3m)z

Juanli Su, Xiaoxue Li
2014 Abstract and Applied Analysis  
Letmbe a positive integer. In this paper, using some properties of exponential diophantine equations and some results on the existence of primitive divisors of Lucas numbers, we prove that ifm>90and3|m, then the equation4m2+1x + 5m2-1y=(3m)zhas only the positive integer solution(x,y,z)=(1,1,2).
doi:10.1155/2014/670175 fatcat:g5de6jrnkbg5vpuo2lretylrfq