On the Diophantine Equation xn+1+ yn+1 = zn+1 + km+1

  IJCOT-book-cover
 
International Journal of Computer & Organization Trends (IJCOT)          
 
© 2014 by IJCOT Journal
Volume - 4 Issue - 1
Year of Publication : 2014
Authors : Dr. J.Kaliga Rani , M.Meenakshi
  10.14445/22492593/IJCOT-V5P307

MLA

Dr. J.Kaliga Rani , M.Meenakshi. "On the Diophantine Equation xn+1+ yn+1 = zn+1 + km+1 ", International Journal of Computer & organization Trends  (IJCOT), V4(1):42-45 Jan - Feb 2014, ISSN:2249-2593, www.ijcotjournal.org. Published by Seventh Sense Research Group.

Abstract—On the Diophantine equation xn+1+ yn+1 = zn+1 + km+1, we analyse the integral solution for some value of m and n with k = 2. Observation found were recorded and presented.

References-

[1]Dicksen, L.E, History of the theory of numbers, vol.II, Chelsea Publishing company, Newyork(1952).
[2]Smith, D.E, History of Mathematics, vol.I and II, Dover Publications, Newyork(1953).
[3]Datta.B and Singh.A.N.,History of Hindu Mathematics Asia Publishing House, Bombay(1938).
[4]Mordell,L.J.,Diophantine Equations, Academic press, Newyork(1969).
[5]Telang.S.G., Number Theory, Tata McGraw-Hill Publishing Company Limited, NewDelhi(1996).
[6]Chen Jian Hua, Complete Solution of the Diophantine Equations X^(2 )+1=dY^(4 ) and a Related Family of Quadratic Thue equations, Journal of number Theory 62(1997),71-99.
[7]Dickson.L.E., History of the Theory of Numbers, Chelsea publishing company, Newyork, 1952.
[8]Leo.J.Alex and Lorraine. L. Foster, On the Diophantine equation 1+p^(a )=2^(b )+2^(c ) p^(d ), Rocky Mountain J. of Math, 15 (3)(1985) 739-761.
[9]Paul van Wamelen, On the CM Character of the curves y^(2 )=x^(q )-1, Journal of Number Theory, 64 (1997) 59-83.
[10]Gopalan.M.A., R.Ganapathy and R.Srikanth, “On the Diophantine Equation Z^(2 )=AX^(2 )+BY^(2 )”, Pure and Applied Mathematics Sciemces, vol.II,No. 1-2, September 2000.
[11]Gopalan.M.A., and Pandichelvi.V., Integral solutions of Ternary Quadratic Equation z(x+y)=4xy., Acta Ciencia Indica, vol.XXXIV M, No 3, 1353(2008).
[12]Goplalan.M.A., Manju Somnath and N.Vanitha., Integral Solutions of Ternary quadratic Diophantine Equation, x^(2 )+y^(2 )=(〖k^(2 )+1)〗^(n ) z^(2 ), Impoact J.Sci.Tech.,vol2(4), 175-178,2008.
[13]Gopalan.M.A., and Kaliga Rani.J., “A Special Pythagorean Triangle”, Acta Ciencia Indica, vol.XXXIV M, No. 2, 867(2008).
[14]Gopalan.M.A., and Kaliga Rani.J., “Observation on the Diophantine Equation Y^(2)=DX^(2)+Z^(2)”, Impact J.Sci. Tech; vol2(2), 91-95,2008.

Keywords—Diophantine equation, integral solutions.