International Journal of Mathematics Trends and Technology
Volume 65 | Issue 1 | Year 2019 | Article Id. IJMTT-V65I1P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I1P503
This paperinvestigates the integer solution of Diophantine Equation (DE). We also discuss the different applications of DE
[1]. Hardy,G.H., and Wright,E.M., An Introduction to the Theory of Numbers, 5th ed., Clarendon Press, Oxford, New York, 1979.
[2]. Mendelsohn, N. S., A Linear Diophantine Equation with Applications to Non‐Negative Matrices, Annals of the New York Academy of Science, September 1970, pp. 287-294.
[3]. Bond, J., Calculating the General Solution of a Linear Diophantine equation, The American Mathematical Monthly, 1967 – JSTOR.
[4]. David Papp, Effective Solution of Linear Diophantine Equation Systems with an Application in Chemistry, Journal of Mathematical Chemistry, Vol. 39, No. 1, January 2006.
[5]. U. Banerjee, Dependence Analysis for Supercomputing, Chapter-5. Linear Diophantine Equations, Kluwer Academic Publishers, 1988, pp. 67-99.
[6]. Joseph H.Silverman, A Friendly Introduction To Number Theory, Precentice-Hall,Inc., New Jersey, 2001.
[7]. H.E.Rose, A Course In Number Theory,Clarendon Press, New York, 1994.
[8]. William Judson Leveque, Topics In Number Theory, Addison-Wesley Publishing Company, USA, 1958.
[9]. Ivan Niven, Herbert S.Zuckerman, An Introduction To The Theory Of Numbers, John Wiley Sons,Inc., USA, 1967.
[10]. Kenneth H.Rosen, Elemantary Number Theory And Its Applications, Greg Tobin, USA, 2005.
[11]. Peter J.Eccles, An Introduction To Mathematical Reasoning:Numbers,Sets And Functions, Cambridge University Press, United Kingdom, 1997.
[12]. Neville Robins, Beginning Number Theory, Jones And Barlett Publishers, USA, 2006.
[13]. M. Clausen, A. Fortenbacher: Efficient solution of linear Diophantine equations. J. Symbolic Comput. 8 (1989), 201–216.
[14]. M. Filgueiras, A. P. Tom´as: A fast method for finding the basis of non-negative solutions to a linear Diophantine equation. J. Symbolic Comput., 19 (1995), 507– 526.
[15]. M. Henk, R. Weismantel: On minimal solutions of linear Diophantine equations. Beitr. Alg. Geom. 41 (2000), 49–55.
[16]. R. Stanley: Linear homogeneous Diophantine equations and and magic labelings of graphs. Duke Math. J. 40 (1973), 607–632.
U.N. Roy, R. P. Sah, A. K. Sah, S. K. Sourabh, "Linear Diophantine Equation: Solution and Applications," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 1, pp. 9-12, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I1P503
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