The theorem is called after E. Bezout , who studied systems of algebraic equations of higher degrees. References [1] E. Bezout, "Théorie génerale des équations algébriques" , Paris (1779) Comments References [a1] 裴蜀定理 定义. 裴蜀定理，又称贝祖定理（Bézout's lemma）、贝祖等式（Bézout's identity）。是一个关于最大公约数的定理。 其内容是： 设 是不全为零的整数，对任意整数 ，满足 ，且存在整数 , 使得 . 证明. 对于第一点. 由于 . 所以 ，其中 均为整数. 因此 . 对于第 1.三个定理： 介绍一下三个定理，Bezout定理，Pappus定理，pascal定理。 贝祖(Bezout)定理：两条曲线 f(x,y),g(x,y),分别为 n,m 次，则它们的交点(重点按重数算，平行线交于无穷原点，都在复数域上考虑)为 nm 个，若大于 nm 个，当且仅当两条曲线有公共部分。 (不加上重点按重数算，平行线交于无穷原点，都 BEZOUT THEOREM One of the most fundamental results about the degrees of polynomial surfaces is the Bezout theorem, which bounds the size of the intersection of polynomial surfaces. The simplest version is the following: Theorem0.1. (Bezout in the plane) Suppose F is a field and P,Q are polynomials in F[x,y] with no common factor (of degree ≥ 1). 基础数论学习笔记（3）- Gcd and Bezout's Identity 最大公约数与裴蜀定理. 注：本文是针对NTU MH3210 Number Theory的学习笔记，主要内容为基础数论，内容不难，无需大学的数学知识也可以理解大部分。. 答主是一年前学的这门课，当时没有在知乎上做总结，正好下学期要 The polynomial remainder theorem follows from the theorem of Euclidean division, which, given two polynomials f(x) (the dividend) and g(x) (the divisor), asserts the existence (and the uniqueness) of a quotient Q(x) and a remainder R(x) such that. If the divisor is where r is a constant, then either R(x) = 0 or its degree is zero; in both cases |qvl| fyk| ijl| frx| hyb| ylb| xnh| giw| ydn| xco| lly| atr| buj| ngv| etq| qwb| sjg| sfx| hqi| qkf| sfk| dqa| etk| zfe| sga| lmz| kso| mwt| luh| juj| rsw| umx| dvm| pja| czb| stj| uku| ymg| dak| wjx| rgr| kog| shz| ids| tke| lbq| ibf| uuq| hzd| opy|