Solution of the Surd Diophantine Equation $\sqrt[n]{\mathbf{x}}+\sqrt[n]{\mathbf{y}}+\sqrt[n]{\mathbf{z}}+\sqrt[n]{t}=\sqrt[n]{\mathbf{u}}$

Hari Kishan, Surya Gautam and Megha Rani

In this study, the Diophantine equation $\sqrt[n]{\mathbf{x}}+\sqrt[n]{\mathbf{y}}+\sqrt[n]{\mathbf{z}}+\sqrt[n]{t}=\sqrt[n]{\mathbf{u}}$ has been discussed for some positive integral values of n and for rational numbers of the form $\mathrm{n}=\frac{2}{\mathrm{p}}$ , p is a prime number. Integral solutions of Diophantine equation have been obtained for n = $2,3,4,\frac{2}{3}\text{and}\frac{2}{5}$.

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