摘要
运用无穷递降法证明了:方程X4-10X2Y2+5Y4=Z2和X4-50X2Y2+125Y4=Z2都没有适合gcd(X,Y)=1以及2|XY的正整数解(X,Y,Z).由此推知:方程x2+y4=z5没有适合gcd(x,y)=1的正整数解(x,y,z),上述结果解决了广义Ferm at猜想的一个特殊情况。
Using the infinite descent method, we prove that the equations X^4 - 10X^2 Y^2 + 5 Y^4 = Z^2 and X^4 - 50X^2Y^2 + 125Y^4 = Z^2 have no positive integer solution (X,Y,Z) with gcd (X,Y) = 1 and2| XY. It implies that the equation x^2+ y^4= z^5 has no positive integer solution (x,y,z) with gcd (x,y) = 1 . Thus, a special case of the generalized Fermat conjecture is solved.
出处
《云南师范大学学报(自然科学版)》
2009年第4期1-5,共5页
Journal of Yunnan Normal University:Natural Sciences Edition
基金
国家自然科学基金资助项目(10771186)
广东省自然科学基金资助项目(06029035)