不定方程x^2+k^2=y^3的有理整解

On the Rational Integer Solutions of Diophantine Equations x^2+k^2=y^3

利用了数论初等方法,讨论了k是有理素数p≡1mod 4)且k=e2+1,e∈Z为偶数和k是有理素数p≡3(mod4)的相伴数和,方程x2+k2=y3的解的情况。

Using the methods of elementary number theory, It discussed the k is rational prime p ≡ 1 （ rood 4 ） and k=e2＋1,e∈Z, for even and k is rational prime number p ≡3 （ rood 4） companions number, the solution of the e- quation x2 ＋ k2 = y3.