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Scholars Journal of Engineering and Technology | Volume-2 | Issue-05
On Homogeneous Ternary Quadratic Diophantine Equation 4 �2 + �2 − 7�� = 16 �2
M. A. Gopalan, S. Vidhyalakshmi, R. Maheswari
Published: Aug. 30, 2014 | 79 79
DOI: 10.36347/sjet
Pages: 676-680
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Abstract
The ternary quadratic homogeneous equation representing homogeneous cone given by 4 �2 + �2 − 7�� = 16 �2 is analyzed for its non-zero distinct integer points on it. Five different patterns of integer points satisfying the cone under consideration are obtained. A few interesting properties among the solutions and polygonal numbers are presented.