Number theory is strongly reliant on diophantine equations, which can take many different forms. There are a variety of Diophantine equations that have no solution, trivial solutions, a finite number of solutions, and an infinite number of solutions. There are essentially two types of equations among higher degree Diophantine Equations. They are homogeneous and non-homogeneous bi-quadratic equations when the degree is four. Its integral solution may be required in its most basic form. Many mathematicians have been fascinated by both homogeneous and non-homogeneous Biquadratic equations since ancient times. The challenge of identifying non-trivial integral solutions of the non-homogeneous Biquadratic equation with four unknowns provided by 7xy + 3z2 = 3 w4 is addressed in this study. The linear transformations x = u + v, y = u – v, and z = v are used to find an infinite number of non-zero integer solutions to the equation.
Department of Mathematics, Government First Grade College, Koteshwara, Kundapura Taluk, Udupi – 57622, Karnataka, India.
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