多项式环中的Fermat定理

Fermat's Last Theorem in Polynomial Rings

首先介绍了多项式与多项式的基本式之间的一些性质,然后得到了定理:对于交换的无零因子环R,若满足条件:R[x]中任意两个多项式f(x)、g(x)都有最大公因式,那么对于R[x]中的任意互素的多项式f(x)、g(x)、h(x),且不全为常数,以及任何自然数n≥3,等式fn(x)+gn(x)=hn(x)永远不成立。

First,some properties between f（x） and the basic form of f（x） are explained. Then,a theorem is proved：Given a commutative ring without zero divisors satisfaying some conditions, then any two polynomials in R[x] have a greatest common divisor,then for polynomials f（x）,g（x）,h（x） which are mutually prime in R[x] and all are not constants,f^n（x）＋g^n（x）=h^n（x） is never true for all n≥3.