TURKISH JOURNAL OF MATHEMATICS · 2019 · 15 citations · 0 references
Natural SciencesMathematicsDifferential EquationsDiscrete MathematicsDiophantine EquationsDiophantine Equation SolvingExponential Diophantine EquationsIntegral SolutionsLinear Diophantine EquationsPell EquationsPell's EquationPolynomial Diophantine Equations
In this paper, we find all the solutions of the title Diophantine equation in nonnegative integer variables $(m, n, x)$, where $P_k$ is the $k$th term of the Pell sequence.