Integral solution of the ternary cubic equation 6(x2+y2) - 11xy + x + y+ 1+552z3

The ternary cubic condition 6(x2+y2) - 11xy + x + y+ 1+552z3 is considered for deciding its non-zero particular basic arrangements utilizing the linear transformations , and utilizing the strategy for factorization in complex forms, various methods of essential answers for the ternary cubic condition viable are gotten. In each method, fascinating relations among the arrangements, a few exceptional polygonal, pyramidal numbers and focal pyramidal numbers are displayed.