On Homogeneous Ternary quadratic Diophantine Equation a(x2 + y2) - bxy = 4az2, b ≠ 2a a(x2 + y2) - bxy = 4az2, b ≠ 2a

M. A. Gopalan; S. Vidhyalakshmi; R. Maheswari

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ISSN Print: 2394-7500, ISSN Online: 2394-5869, CODEN: IJARPF

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International Journal of Applied Research

Vol. 1, Issue 6, Part B (2015)

On Homogeneous Ternary quadratic Diophantine Equation a(x² + y²) - bxy = 4az², b ≠ 2a a(x² + y²) - bxy = 4az², b ≠ 2a

Author(s)
M. A. Gopalan, S. Vidhyalakshmi, R. Maheswari

Abstract
The ternary quadratic homogeneous equation representing homogeneous cone given by 2a a(x² + y²) - bxy = 4az², b ≠ 2a is analyzed for its non-zero distinct integer points on it. Six different patterns of integer points satisfying the cone under consideration are obtained. A few interesting properties among the solutions and polygonal numbers are presented.

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How to cite this article:

M. A. Gopalan, S. Vidhyalakshmi, R. Maheswari. On Homogeneous Ternary quadratic Diophantine Equation a(x² + y²) - bxy = 4az², b ≠ 2a a(x² + y²) - bxy = 4az², b ≠ 2a. Int J Appl Res 2015;1(6):88-91.

IMPACT FACTOR (RJIF): 8.4

Vol. 1, Issue 6, Part B (2015)

On Homogeneous Ternary quadratic Diophantine Equation a(x² + y²) - bxy = 4az², b ≠ 2a a(x² + y²) - bxy = 4az², b ≠ 2a

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