Abstract
We obtain infinitely many non-zero integer solutions ( , , , , , , ) x y z w X Y T satisfying the non- homogeneous quintic equation with seven unknowns given by 2 2 2 2 2 2 3 xy x y zw z w X Y T ( ) ( ) ( ) . Various interesting relations between the solutions and special numbers, namely, polygonal numbers, Pyramidal numbers, Stella Octangular numbers, Octahedral numbers,, Jacobsthal number, Jacobsthal-Lucas number, keynea number, Centered pyramidal numbers are presented.
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