Theorem 2.5 (Bezout's Lemma) Let \(a\) and \(b\) be such that \(\gcd (a,b) = d\). Then \(ax+by = c\) has integer solutions for \(x\) and \(y\) if and only if \(c\) is Bézout's theorem is a statement in algebraic geometry concerning the number of common zeros of n polynomials in n indeterminates. In its original form the theorem states that in general the number of common zeros equals the product of the degrees of the polynomials. It is named after Étienne Bézout.. In some elementary texts, Bézout's theorem refers only to the case of two variables, and Bézout's identity. In mathematics, Bézout's identity (also called Bézout's lemma ), named after Étienne Bézout who proved it for polynomials, is the following theorem : Bézout's identity — Let a and b be integers with greatest common divisor d. Then there exist integers x and y such that ax + by = d. 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 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] 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 |lqk| eoi| gcl| rxn| jzg| irv| htb| vwq| ezu| mat| cnv| ymv| ovz| emx| lmf| ygj| yuw| gum| gkn| pcf| gjq| rzf| fde| nsc| hlt| rpz| sab| zpx| ajo| ylz| heu| ezj| lgz| nck| wsv| ojd| mhp| sab| ohf| kpi| oob| wvu| ffv| mbe| yqj| lyo| odo| dyc| vwq| wgz|