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On the Diophantine Equation X2 + 13K = YN
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The object of this paper is to find all solutions of the dio-phantine equation x2 + 13k = yn, in positive integers x, y with n ≥ 3.
Keywords
Primitive Divisor Theorem of Carmicheal, Theorem of Catalan, Nagell Equation
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- F.S. Abu Muriefah, F. Luca, A. Togbe, On the Diophantine equation x2 + 5a13b = yn, Glasgow Math. J. 50 (2008), 175-181.
- S.A. Arif and F. S. Abu Muriefah, On the Diophantine equation x2 + q2k+1 = yn, The Arabian J. for Sci. and Engineering, 26(1A), 53-62, 2001.
- S.A. Arif and F.S. Abu Muriefah, On the Diophantine equation x2 + q2k = yn, Journal of Number Theory, 95(1), 95-100, 2002.
- A. Berczes, I. Pink, On the Diophantine equation x2 +p2k = yn, Arch. Math. 91 (2008) 505-517.
- Y.F. Bilu, G. Hanrot, P.M. Voutier, Existence of primitive divisors of Lucas and Lehmer numbers, J. Reine Angew. Math., 539, 75-122, 2001.
- Y. Bugeaud, F. Luca, M. Mignotte, S. Siksek, Almost Powers in the Lucas Sequence. Journal de Theorie des Nombres de Bordeaux. 20 (2008), no 3, 555-600.
- H. Cohen, Explicit Methods for Solving Diophantine Equations. Tucson, Arizona Winter School, 2006.
- J.H.E. Cohn, The Diophantine equation x2 + C = yn, Acta Arith. 65 (1993), No.4, 367-381.
- J.H.E. Cohn, The Diophantine equation x2+C = yn, Acta Arith., 65(4), 367-381, 1995.
- E. Goins, F. Luca, A. Togbe, On the Diophantine equation x2 + 2α5β13γ = yn, ANTS VIII Proceedings: A. J. van der Poorten and A. Stein (eds.), ANTS VIII, Lecture Notes in Computer Science 5011 (2008), 430-442.
- Hui Lin Zhu, Mao Hua Lec, On some generalized Lebesgue-Nagell equations. Journal of Number Theory 131 (2011) 458-469.
- F. Luca, On the Equation x2 +2a3b = yn, Int. J. Math. Math. Sci. 29.4 (2002) 239-244
- F. Luca, A. Togbe, On the Diophantine equation x2 +72k = yn, Fibonacci Quart., no. 4, 322-326 (2008).
- F. Luca, Eective methods for Diophantine equations, Universidad Nacional Autonoma de Mexico (2009)
- T. Nagell, Contributions to the theory of a category of Diophantine equations of the second degree with two unknown, Nova Acta Reg. Soc. Upsal. Ser. 4 (1955), no.16, 1-38.
- S. Siksek, J.E. Cremona, On the Diophantine equation x2 + 7 = ym, Acta Arith. 109 (2) (2003) 143-149.
- L. Tao, On the Diophantine equation x2 + 5m = yn, Ramanujan J. 19 (2009) 325-338.
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