Adel Alahmadi, Florian Luca: On the Diophantine equation $(5pn^2-1)^x+(p(p-5)n^2+1)^y=(pn)^z$, 3-12


We find all solutions of the Diophantine equation in the title in positive integers $(x,y,z,p,n)$ where $p>3$ is a prime.

Key Words: Diophantine equations, applications of Baker's method, primitive divisors of Lucas sequences.

2010 Mathematics Subject Classification: Primary 11D61; Secondary 11J86.

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