The ternary quadratic homogeneous equation representing homogenous cone given by 2 2 2 z ? 45x ? y is analyzed for its non-zero distinct integer points on it. Four different patterns of integer points satisfying the cone under consideration are obtained. A few interesting relations between the solutions and special number patterns namely Polygonal number, Pyramidal number, Octahedral number, Stella Octangular number and Oblong number are presented. Also knowing an integer solution satisfying the given cone,two triples of integers generated from the given solution are exhibited.
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