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While a method of obtaining numerical solutions of such an equation has recently been given, it seems that an explicit parametric of this diophantine equation has not yet been published. We obtain a multi-parameter solution of this equation for arbitrary values of $a_i$ and for any positive integer $n \\geq 3$, and deduce specific solutions when $n=3$ and $n=4$. 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While a method of obtaining numerical solutions of such an equation has recently been given, it seems that an explicit parametric of this diophantine equation has not yet been published. We obtain a multi-parameter solution of this equation for arbitrary values of $a_i$ and for any positive integer $n \\geq 3$, and deduce specific solutions when $n=3$ and $n=4$. 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