In this article we show that the form $x^2 + iy^2 + z^2 + iw^2$ representsall gaussian integers. The main tools used in this proof are Fermat's littletheorem (over finite field extensions), the Mordell-Niven theorem(representation of some gaussians), and the generalized Euler-identity overfinite field extensions.
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机译：在本文中，我们证明$ x ^ 2 + iy ^ 2 + z ^ 2 + iw ^ 2 $的形式表示所有高斯整数。该证明中使用的主要工具是Fermat的littletheorem定理（在有限域扩展上），Mordell-Niven定理（一些高斯的表示）和广义Euler-恒等式超界扩展。
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