关于不定方程x^2+4~n=y^(13)(n=4,5,6)的整数解

The integer solution on Diophantine equation x^2+4~n=y^(13)(n=4,5,6)

在高斯整环中,利用代数数论与同余理论的方法,讨论了不定方程x^2+4~n=y^(13)(n=4,5,6)的整数解问题,得出了当n=4,5时无整数解;n=6是仅有整数解(x,y)=(64,2)和(x,y)=(-64,2)的结论,推进了不定方程整数解的研究.

In the Gauss domain,using the method of algebraic number theory and congruence theory,we discuss the problem of integer solution of Diophantine equation x2+4n=y13(n=4,5,6):We obtained when n=4,5,x2+4n=y13has no integer solution,when n=6,x2+4n=y13has only integer solution(x,y)=(±64,2),which advanced the study of Diophantine equation.