关于不定方程x^2+4~n=y^5

On the Indefinite Equation x^2+4~n=y^5

用代数数的方法证明了不定方程x2+4n=y5仅有解(n,x,y)=(5m,0,4m),(5m+2,±25m+2,2.4m).

In this paper,the author has proved that the indefinite equation x2＋4n=y5 has only integer solution（n,x,y）=（5m,0,4m）,（5m＋2,±25m＋2,2·4m）（m∈N）.