Abstract
Let \(p\) be an odd prime. In this paper we study the integer solutions \((x,y,n,a,b)\) of the equation \(x^{2}+2^{a}p^{b}=y^{n}, x\ge 1,y>1,\gcd (x,y)=1,a\ge 0,b\ge 0,n\ge 3\).
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Acknowledgments
The authors would like to thank the referee for the suggestions to improve this paper. The first author was partly supported by the Fundamental Research Funds for the Central Universities (No. 2012121004) and the Science Fund of Fujian Province (No. 2012J050009, 2013J05019). The second author was supported by NSFC (No. 10971184). The third author was supported by the research fund of Uludağ University Project (No. F-2013/87). The work on this paper was completed during a very enjoyable visit of the fourth author at The Institute of Mathematics of Debrecen. He thanks this institution and Professor Ákos Pintér for the hospitality. He was also supported in part by Purdue University North Central.
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Zhu, H., Le, M., Soydan, G. et al. On the exponential Diophantine equation \(x^{2}+2^{a}p^{b}=y^{n}\) . Period Math Hung 70, 233–247 (2015). https://doi.org/10.1007/s10998-014-0073-9
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DOI: https://doi.org/10.1007/s10998-014-0073-9