On the Non-Homogeneous Quintic Equation with Seven Unknowns xy(x2+y2)+zw(z2+w2) = (X2+Y2)T3
S. Vidhyalakshmi1, M. A. Gopalan2, K. Lakshmi3
1Prof. Dr. S. Vidhyalakshmi, Department of Mathematics, Shrimati Indira Gandhi College, Trichy, Tamil Nadu, India.
2Prof. Dr. M. A. Gopalan,, Department of Mathematics, Shrimati Indira Gandhi College, Trichy, Tamil Nadu, India.
3K. Lakshmi, Lecturer, Department of Mathematics, Shrimati Indira Gandhi College, Trichy, Tamil Nadu, India.
Manuscript received on April 30, 2015. | Revised Manuscript received on May 04, 2015. | Manuscript published on May 15, 2015. | PP: 12-15 | Volume-3 Issue-6, May 2015. | Retrieval Number: F0855053615/2015©BEIESP
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Abstract: FWe 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 xy(x2+y2)+zw(z2+w2) = (X2+Y2)T3. 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
Keywords: Centered pyramidal numbers, Integral solutions, Non-homogeneous Quintic equation, Polygonal numbers, Pyramidal numbers MSC 2010 Mathematics subject classification: 11D41.