DOI: 10.36347/sjpms

Pages: 84-87

The non-homogeneous octic equation with five unknowns represented by the diophantine equation x4  y4  T 6(z2  w2)is analyzed for its patterns of non-zero distinct integral solutions and two different patterns of integral solutions are illustrated. Various interesting relations between the solutions and special numbers, namely, Pyramidal numbers, Pronic numbers, Stella octangular numbers, Gnomonic numbers, polygonal numbers, fourth, fifth and sixth dimensional figurate numbers are exhibited. Keywords: Octic non-homogeneous equation, Pyramidal numbers, Pronic numbers, Fourth, fifth and sixth dimensional figurate numbers. M.Sc 2000 mathematics subject classification: 11D41