【简答题】![](https://cos-cdn.shuashuati.com/shuashuati-web/2024-0521-0905-00/logo-new-ad743.png)
证明:如果f1(x),f2(x),...,fs-1(x)的最大公因式存在,那f1(x),f2(x),...,fs-1(x),fs(x)的最大公因式也存在,且当f1(x),f2(x),...,fs(x)全不为零时有
(f1(x),f2(x),...,fs-1(x),fs(x))=((f1(x),f2(x),...,fs-1(x)),fs(x)).在利用上式证明,存在多项式u1(x),u2(x),...,us(x)使
![](https://cdn.shuashuati.com/imgs/33d2e68a56b6032faba06c13ce603af0.jpg)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAgCAYAAABzenr0AAAA5ElEQVRYR2NkGGDAOMD2M+B0wKpVq9huv/jbxPD/fxwDA4MkhQ59zsDIuEhVgrkuLCzsF7JZOB3QOml5B8P//+UUWoyqnZGxszovsoI4B0xc9gyfzxmZmb2rcsK3IRvWMWm599///7fgcfTz6vwoKWId8B+f75kZGX0q8iK3kugAhur8KJRQxx0FE5fhdQC5UTPqgNEQGA2B0RAYDYHREBgNgaETAuTW96TqG7yt4tbRFhGRIQBqHTP9+8dIoDUMTxqk5AK8zXKYiaDWMYhNpANIaJYPdMdkwLtmpOZnctUPeDkAAP6tmiH1ggTLAAAAAElFTkSuQmCC)
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参考答案:
![](https://cos-cdn.shuashuati.com/shuashuati-web/2024-0521-0905-00/logo-new-ad743.png)
参考解析:
![](https://cos-cdn.shuashuati.com/shuashuati-web/2024-0521-0905-00/logo-new-ad743.png)