费尔马最后定理的证明

The Proof of Fermat's Last Theorem

（ｉ）我们用（ｘ－ｂ）ｎ＋ｘｎ＝（ｘ＋ａ）来代替ｘｎ＋ｙｎ＝ｚｎ作为费尔马最后定理（ＦＬＴ）的普遍方程式．其中ａ及ｂ是两个任意自然数．应用二项展开式，（０．１）可以写成因为ａｒ－（－ｂ）ｒ始终包含ａ＋ｂ作为它的因数，（０．２）可写成其中фｒ＝［ａｒ－（－ｂ）ｒ］／（ａ＋ｂ）对于ｒ＝１，２，…，ｎ．都是个整数．（ｉｉ）令ｓ是ａ＋ｂ的一个因数，并令ａ＋ｂ＝ｓｃ．我们可用ｘ＝ｓｙ来变换（０．３）成为下列（０．４）（ｉｉｉ）将（０．４）除以Ｓ２，我们得（０．５）式的左边，是的整系数多项式，而右边ｃф／ｓ是个常数Ｃф／ｓ．若Ｃф／ｓ不是个整数，那末我们不能求得能适合（０．５）的整数ｙ，这样ＦＬＴ对这场合是对问．若Ｃфｎ／ｓ是个整数，我们可以改变ｓ和ｃ，使ｃф／ｓ≠整数。

i)Instead of xn+yn=Zn,we use as theorem(FLT),where a and b are two arbitrary natural numbers by means o fbinomial expansion can be writtenasbecause ar --b alway contains a+bas its factor can be writtenas weher are in tegers for r=1,2,3…,n (ii)Let s be a factor of a+b and let (a+b)=sc .We can use x=sy to trans-form (0.3) to the following (0. 4)(iii) dividing (0.4) by s2, we haveOn the left side of(0.5), there is a polynomial of U with integer coefficients and on the right side there is a constant cф/s. If cфn/s is not an integer,then we cannot find an integer y to satisfy (0.5), and then FLT is true for thiscase. If cфn/s is an integer, we may change s and c such that c&./span integer.