关于不定方程x^2+64=4y^n(n=7,11)的解

The Solution on Diophantine Equation x^2+64=4y^n( n= 7,11)

不定方程整数解的问题是数论方面的一个重要分支,利用代数数论和同余的方法讨论不定方程x^2+64=4y^n(x,y∈Z),当n=7,11时整数解的问题,并证明了不定方程x^2+64=4y^n(n=7,11)无整数解.

The integer solution to Diophantine equation is an important branch of the number theory, the problem of integer solution to the Diophantine equation x^2 ＋64 = 4y^n（x ,y ∈Z） is discussed by using the methods of algebraic number theory and congruence when n = 7,11. and that the Diophantine equation x^2＋64 = 4y^n（ n = 7,11 ） has no integer solution is proved.