DOI: 10.36347/sjpms

Pages: 104-107

The non-homogeneous biquadratic equation with four unknowns given by x y z x y W 3 3 3 3     128( ) is considered and analysed for its non-zero distinct integer solution, Introducing the linear transformation x u v y u v z u      ; ; 2 and employing the method of factorization different patterns of non-zero distinct integer solutions to the above biquadratic equation are obtained. A few interesting relations between solutions and special numbers namely Centered Polygonal numbers, Polygonal numbers, ,Mersenne number are exhibited.. Keywords: Non-Homogeneous biquadratic equation, Integral solutions, Special numbers