关于费马大定理(Ⅱ)

ON FERMAT'S LAST THEOREM (II)

证明了方程x^(2p)+y^(2p)=z^2((x,y)=1,P(>3)是素数)如有解,则必有4P^2|x或4P^2|y.对方程x^(2p)+y^2=z^(2p),x^(2p)+y^(2p)=z^p和x^(2p)+y^p=z^(2p)也得到了类似的结果.此外,我们还有以下的结果:(1)设r(N)表示使得方程x^(2n)+y^(2n)=z^2有解的正整数n(≤N)的个数,则r(N)=o(N)(N→∞).(2)如果正整数x,y,z和n满足x^n+y^n=z^n,x<y<z,n>2,则必有x^2>nz+n-3.

In this paper, it has been proved that if the equationx2p + y2p=z2 (x, y) =1 and a prime p>3 (1)has integer solution, then 4p2|x or 4 P2|y. For the equationsx2p + y2=z2p, x2p + y2p=z2p and x2p +yp = z2pthe results which are analogous to (1) are also established. In addition, other two results are also obtained:1. Let r(N) be the number of n<N with the equation x2n+y2n=z2 has integer solution. Then r(N)=o(N). as N→∞.2. If the equation xn + yn= zn has a solution in positive integers x<y<z for some n>2, them x2>nz + n-3.