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OBSERVATIONS ON THE NONHOMOGENEOUS QUINTIC EQUATION WITH FIVE UNKNOWNS

S.Vidhyalakshmi , S.Mallika , M.A.Gopalan

The quintic Diophantine equation with five unknowns 4 4 2 2 2 2 3 x � y � 2(k � s )(z �w )p is analyzed for its infinitely many non-zero distinct integral solutions. A few interesting relations between the solutions and special numbers namely, centered polygonal numbers, centered pyramidal numbers, jacobsthal numbers, Lucas numbers and Keynea numbers are presented.