On The Homogeneous Biquadratic Equation with 5 Unknowns

Dr. P. Jayakumar, J. Meena

Abstract: The Homogenous biquadratic equation with five unknowns given by is considered and analyzed for finding its non zero distinct integral solutions. Introducing the linear transformations x = u + v, y = u v, z = 2uv +1, w =2uv-1 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, Star number, Pronic number and Gnomonic number are exhibited.

Keywords: Homogeneous equation, Integral solutions, Polygonal number and special number

How to Cite?: Dr. P. Jayakumar, J. Meena, "On The Homogeneous Biquadratic Equation with 5 Unknowns ", Volume 4 Issue 12, December 2015, International Journal of Science and Research (IJSR), Pages: 656-658, https://www.ijsr.net/getabstract.php?paperid=NOV151842, DOI: https://dx.doi.org/10.21275/NOV151842