%0 Journal Article
%T 分担集合的多项式的惟一性<br>The Uniqueness of Polynomial Sharing a Set
%A 刘丹
%A 林威扬
%J Pure Mathematics
%P 295-299
%@ 2160-7605
%D 2013
%I Hans Publishing
%R 10.12677/PM.2013.35045
%X <div style=\"text-align:justify;\">
	<span style=\"line-height:1.5;\">本文研究了</span><span style=\"line-height:1.5;\">Gross</span><span style=\"line-height:1.5;\">在</span><span style=\"line-height:1.5;\">1976</span><span style=\"line-height:1.5;\">年所提出的一个惟一性问题关于多项式的情形，证明了存在三个元素的集合</span><span style=\"line-height:1.5;\">S</span><span style=\"line-height:1.5;\">，使得对于任何两个非常数多项式</span><span style=\"line-height:1.5;\">f</span><span style=\"line-height:1.5;\">和</span><span style=\"line-height:1.5;\">g</span><span style=\"line-height:1.5;\">，如果</span><span style=\"line-height:1.5;\">f</span><span style=\"line-height:1.5;\">, </span><span style=\"line-height:1.5;\">g </span><span style=\"line-height:1.5;\">CM</span><span style=\"line-height:1.5;\">分担</span><span style=\"line-height:1.5;\">S</span><span style=\"line-height:1.5;\">，则</span><span style=\"line-height:1.5;\">。并且集合</span><span style=\"line-height:1.5;\">S</span><span style=\"line-height:1.5;\">的基数</span><span style=\"line-height:1.5;\">3</span><span style=\"line-height:1.5;\">是最佳的。&lt;br/</span><span style=\"line-height:1.5;\">&gt;</span><span style=\"line-height:1.5;\">This paper studied the uniqueness of polynomial posed by Gross in 1976, and proved that there exists a set </span><span style=\"line-height:1.5;\">S</span><span style=\"line-height:1.5;\"> </span><span style=\"line-height:1.5;\">with 3 elements such that for any two non-constant polynomials </span><span style=\"line-height:1.5;\">f</span><span style=\"line-height:1.5;\"> and </span><span style=\"line-height:1.5;\">g</span><span style=\"line-height:1.5;\">, if </span><span style=\"line-height:1.5;\">f</span><span style=\"line-height:1.5;\"> and </span><span style=\"line-height:1.5;\">g</span><span style=\"line-height:1.5;\"> share </span><span style=\"line-height:1.5;\">S</span><span style=\"line-height:1.5;\"> CM, then </span><span style=\"line-height:1.5;\">. And the number 3 of the set </span><span style=\"line-height:1.5;\">S</span><span style=\"line-height:1.5;\"> is best possible.</span>
</div>
%K 多项式；分担值；CM分担；惟一性<br>Polynomial
%K Shared Value
%K CM Sharing
%K Uniqueness
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=12324