DOI: 10.36347/sjet

Pages: 9-13

The ternary quadratic homogeneous equation representing homogeneous cone given by 59x2  y2  z2 by is analyzed for its non-zero distinct integer points on it. Three 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, Pronic number, Stella Octangular number, Pentatope number and Nasty number are presented. Also knowing an integer solution satisfying the given cone, three triples of integers generated from the given solution are exhibited.