On Non-Homogeneous Cubic Diophantine Equation 5x2 + 5 y2 – 9xy = 23z3

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Year:
2016
Type of Publication:
Article
Keywords:
The Method of Factorization, Integer Solutions, Linear Transformation, Relations and Special Numbers
Authors:
Dr. P. Jayakumar; V. Pandian
Journal:
IJISM
Volume:
4
Number:
2
Pages:
102-104
Month:
March
ISSN:
2347-9051
Abstract:
Four different methods of the non-zero non-negative solutions of non- homogeneous cubic Diophantine equation 5x2 +5y2 –9 x y = 23z3 are exposed. Introducing the linear transformation x = u + v, y = u – v, u  v 0 in 5x2 +5y2 – 9 x y = 23z3,it reduces to u2 +19v2 = 23z3. We are solved the above equation through various choices and the different methods of solutions which are satisfied it. Some interesting relations among the special numbers and the solutions are observed. The following notations are used: tn,m = Polygonal number of rank n with sides m- Gn= Gnomonic number of rank n – Pnm = Pyramidal number of sides n with rank m 2010 Mathematics subject classification: 11D25

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