In this paper, we prove that there is no x>=4 such that the difference of x-th powers of two consecutive Fibonacci numbers greater than 0 is a Lucas number.
An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers
On some conjectures of exponential Diophantine equations
An Exponential Diophantine equation $x^2+3^α 113^β=y^{\mathfrak{n}}$
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