On the Non-Homogeneous Equation of the Eighth Degree with Six Unknowns x5 -y 5 +(x3 -y 3)xy = p(z2 -w 2) 2T 3

We obtain infinitely many non-zero integer sextuples( , , , , , ) x y z w p T satisfying the non-homogeneous equation of degree eight with six unknowns given by 5 5 3 3 2 2 2 3 x y x y xy p z w T − + − = − ( ) ( ) . Various interesting relations between the solutions and special numbers, namely, polygonal numbers, Pyramidal numbers, Star numbers, Stella Octangular numbers, Octahedral numbers, Pronic number, Jacobsthal number