Luca, Florian On a Diophantine equation. (English) Zbl 0997.11027 Bull. Aust. Math. Soc. 61, No. 2, 241-246 (2000). 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 \(n=3\). Reviewer: Edward L.Cohen (Ottawa) Cited in 13 Documents MSC: 11D61 Exponential Diophantine equations 11B39 Fibonacci and Lucas numbers and polynomials and generalizations Keywords:exponential Diophantine equation PDF BibTeX XML Cite \textit{F. Luca}, Bull. Aust. Math. Soc. 61, No. 2, 241--246 (2000; Zbl 0997.11027) Full Text: DOI OpenURL References: [1] Lebesgue, Nouv. Annal. des Math 9 pp 178– (1850) [2] Ko, Sci. Sinica 14 pp 457– (1965) [3] DOI: 10.1155/S0161171298000866 · Zbl 0905.11017 [4] Cohn, Glasgow Math. J 35 pp 203– (1993) [5] Arief, Bull. Austal. Math. Soc 57 pp 189– (1998) [6] Cohn, Acta. Arith 65 pp 367– (1993) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.