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THE DIOPHANTINE EQUATION

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초록

The object of this paper is to give a new proof of all the solutions of the Diophantine equation x² + 11m = yⁿ,in positive integers x; y with odd m > 1 and n ≥ 3.

Abstract

The object of this paper is to give a new proof of all the solutions of the Diophantine equation x² + 11m = yⁿ,in positive integers x; y with odd m > 1 and n ≥ 3.

참고문헌 (26)

  1. Lebesgue, V.A, "Sur I’impossibilité en nombres entieres de I’l equation xm = y2 + 1", Nouvelles Ann. des. Math., 9(1), pp.178~181 (1850)
  2. Nagell, T, "Contributions to the theory of a category of diophantine equa-tions of the second degree with two unknown", Nova Acta Reg. Soc. Upsal. Ser., 4(16), pp.1~38 (1955)
  3. Arif, S.A, "The Diophantine equation x2 + 3m = yn", Int. J. Math. Math. Sci., 21, pp.619~620 (1998)
  4. Arif, S.A, "The Diophantine equation x2 +52k+1 = yn", Indian J. Pure Appl. Math., 30, pp.229~231 (1999)
  5. Arif, S.A, "On the Diophantine equation x2 + q2k+1 = yn", J. Number Theory, 95, pp.95~100 (2002)
  6. Muriefah, F.S. Abu, "The Diophantine equation x2+C = yn", Rev. Colombiana Math., 40, pp.31~37 (2006)
  7. Bugeaud, Y, "On some exponantial Diophantine equations", Monatsh. math., 132, pp.93~97 (2001)
  8. Landau, E, "On the Diophantine equation ay2+by+c = dxn", Proc. London Math.Soc., 19(2), pp.276~280 (1920)
  9. Mignotte, M, "On the Diophantine equations x2 +74 = y5 and x2 + 86 = y5", Glasgow Math. J., 38, pp.77~85 (1996)
  10. Bugeaud, Y, "Classical and modular approaches to exponantial Diophantine equations II", The Lebesque- Nagell equation, Compositio. Math., 142, pp.31~62 (2006)
  11. Tengley, S.Z, "On the Diophantine equation x2 + a2 = 2yp", Indag. Math.(N.S.), 15, pp.291~304 (2004)
  12. Muriefah, F.S. Abu, "The Diophantine equation x2 + q2k = yn", Arab. J. Sci. Eng. Sect. A Sci., 26, pp.53~62 (2001)
  13. Luca, F, "On the equation x2 +2a3b = yn", Int. J. Math. and Math. Sci., 29(4), pp.239~244 (2002)
  14. Luca, F, "On the Diophantine Equation x2 + 2a5b = yn; Int. J. Number Theo., appear", ~
  15. Muriefah, F.S. Abu, "On the Diophantine equation x2 + 5a13b = yn", Glasgow Math. J., 50, pp.175~181 (2008)
  16. Pink, I, "On the Diophantine equation x2 + 2a3b5c7d = yn", Publ. Math. Debrecen, 70(1), pp.149~166 (2007)
  17. Muriefah, F.S. Abu, "On the Diophantine equation x2 + C = 2yn, submitted", ~
  18. Muriefah, F.S. Abu, "On the Diophantine equation px2 + q2m = yp", J. Number Theory, 128, pp.1670~1675 (2008)
  19. Le, M, "On Cohn’s conjecture concerning the Diophantine equation x2 + 2m = yn", Arch. Math(Basel), 78, pp.26~35 (2002)
  20. Cohn, J, "The Diophantine equation x2 + 2k = yn", Arch. Math(Basel), 59, pp.341~344 (1992)
  21. Luca, F, "On a diophantine equation", Bull. Aus. Math. Soc., 61, pp.241~246 (2000)
  22. Muriefah, F.S. Abu, "On a diophantine equation", Bull. Aus. Math. Soc., 57, pp.189~198 (1998)
  23. Arif, S.A, "On Diophantine equation x2 + 2k = yn", Int. J. Math. Math. Sci., 20(2), pp.299~304 (1997)
  24. Luca, F, "On the Diophantine equation x2 + 72k = yn; The Fibonacci Quarterly (2008), preprint", ~ (2008)
  25. Muriefah, F.S. Abu, "On the Diophantine equation x2 + 52k = yn", Demonstratio Math., 319(2), pp.285~289 (2006)
  26. Goins, E, "On the Diophantine equation x2+2 5 13 = yn", Lecture Notes in Computer Science, 5011, pp.430~442 (2008)

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