%0 Journal Article %1 noauthororeditor %A Gopalan, M. A. %A Geetha, K. %A Somanath, Manju %D 2015 %E Kumar, Dr. Shiv %J International Journal of Innovative Science and Modern Engineering (IJISME) %K %N 8 %P 6-10 %T On the Homogeneous Biquadratic Equation with 5 Unknowns %U https://www.ijisme.org/wp-content/uploads/papers/v3i8/H0914073815.pdf %V 3 %X The homogeneous biquadratic equation with five unknowns given by           2 2 2 2 2 2 2 x y k x y k xy k p q z 4 1 4 2 2 4 1               is considered and analyzed for finding its non zero distinct integral solutions. Introducing the linear transformations x u v   , y u v   , p u v   2 , q u v   2 and employing the method of factorization different patterns of non zero distinct integer solutions of the equation under the above equation are obtained. A few interesting relations between the integral solutions and the special numbers namely Polygonal numbers, Pyramidal numbers, Centered Polygonal numbers, Centered Pyramidal numbers, Thabit-ibn-Kurrah number, Carol number, Mersenne number are exhibited.

@article{noauthororeditor, abstract = {The homogeneous biquadratic equation with five unknowns given by           2 2 2 2 2 2 2 x y k x y k xy k p q z 4 1 4 2 2 4 1               is considered and analyzed for finding its non zero distinct integral solutions. Introducing the linear transformations x u v   , y u v   , p u v   2 , q u v   2 and employing the method of factorization different patterns of non zero distinct integer solutions of the equation under the above equation are obtained. A few interesting relations between the integral solutions and the special numbers namely Polygonal numbers, Pyramidal numbers, Centered Polygonal numbers, Centered Pyramidal numbers, Thabit-ibn-Kurrah number, Carol number, Mersenne number are exhibited.}, added-at = {2021-09-18T13:32:46.000+0200}, author = {Gopalan, M. A. and Geetha, K. and Somanath, Manju}, biburl = {https://www.bibsonomy.org/bibtex/24eb9a4d30646a6bfbdd106a7a9b401d5/ijisme_beiesp}, editor = {Kumar, Dr. Shiv}, interhash = {cdba7afdf6cb3a5bd648c7988b1c1393}, intrahash = {4eb9a4d30646a6bfbdd106a7a9b401d5}, issn = {2319-6386}, journal = {International Journal of Innovative Science and Modern Engineering (IJISME)}, keywords = {}, language = {En}, month = {July}, number = 8, pages = {6-10}, timestamp = {2021-09-18T13:32:46.000+0200}, title = {On the Homogeneous Biquadratic Equation with 5 Unknowns }, url = {https://www.ijisme.org/wp-content/uploads/papers/v3i8/H0914073815.pdf}, volume = 3, year = 2015 }