کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4587903 | 1334164 | 2007 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The Casas-Alvero conjecture for infinitely many degrees
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Over a field of characteristic zero, it is clear that a polynomial of the form d(X−α) has a non-trivial common factor with each of its d−1 first derivatives. The converse has been conjectured by Casas-Alvero. Up to now there have only been some computational verifications for small degrees d. In this paper the conjecture is proved in the case where the degree of the polynomial is a power of a prime number, or twice such a power.Moreover, for each positive characteristic p, we give an example of a monic polynomial of degree d which is not a dth power but which has a common factor with each of its first d−1 derivatives. This shows that the assumption of characteristic zero is essential for the converse statement to hold.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 316, Issue 1, 1 October 2007, Pages 224-230
Journal: Journal of Algebra - Volume 316, Issue 1, 1 October 2007, Pages 224-230