关于不定方程x^2+7=4y^3

On the diophantine equation x^2+7=4y^3

对某些d,若Q(d^(1/2))是Euclid域,则在其对应的Euclid整环■(d^(1/2))中算术基本定理成立。利用此来证明不定方程x2+7=4y3有惟一正整数x=5,y=2。

For somed,if Q(d^(1/2)) is Euclidean field,inaccording Euclidean domain ■(d^(1/2)),arithmetical funda-mental theoremis carried out.Mainly usingthe method todiscuss the integer solution of diophantine equationx2+7 =4y3,and we will get the unique integer solutionthatx=5,y=2.