On a Diophantine equation. (English) Zbl 0997.11027

All solutions are found of the Diophantine equation \(x^2+ 3^m= y^n\), where \((x,y,m,n)\) are nonnegative integers with \(x\neq 0\) and \(n\geq 3\). The proof uses the following Theorem: All solutions of the above equation with \(m\) even are of the form \(x= 46\cdot 3^{3t}\), \(m= 4+6t\), \(y= 13\cdot 3^{2t}\) and \(n=3\).


11D61 Exponential Diophantine equations
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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