  This paper is concerned with the diophantine equation $\sum_{i=1}^na_ix_i^4=
\sum_{i=1}^na_iy_i^4$ where $n \geq 3$ and $a_i,\,i=1,\,2,\,\ldots,\,n$, are
arbitrary integers. 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 $n=4$. The
numerical solutions thus obtained are much smaller than the integer solutions
of such equations obtained earlier.
