Integral Solutions of the Homogeneous Biquadratic Diophantine Equations with Five Unknowns (X2 - Y2) (3X2 + 3Y2 ?2XY) = 12(Z2 ?W2)T2

Dr. P. Jayakumar, G. Shankarakalidoss

Abstract: Four different patterns are used to find non-zero distinct integral solutions for the homogeneous biquadratic Diophantine equations (X2 - Y2) (3X2 + 3Y2 2XY) = 12 (Z2 W2) T2. Different types of properties are exposed in every pattern with polygonal, nasty, square and cubic numbers.

Keywords: Homogeneous biquadratic, integral solutions, special numbers