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The homogeneous cubic equation with four unknowns represented by the Diophantine equation x3+y3= 2lzw2 is analyzed for its patterns of non – zero distinct integer solutions. A few interesting properties between the solutions and special numbers, namely, Polygonal number, Pyramidal number, Centered polygonal number, Stella octangular number and Octahedral number are presented.
Gopalan et al. (Wed,) studied this question.