Abstract
This paper focuses on obtaining non-zero integer quintuples (x,y, z,w, p) satisfying the bi-quadratic equation with ve unknowns given by 2(x - y)(x3 + y3) + x4 - y4 = 2(z2 - w2)p2. Various patterns of solutions are obtained by reducing the given bi-quadratic equation to solvable ternary quadratic equation through employing linear transformations.
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