丢番图方程x^3+64=3y^2的整数解

On Integer Solution of the Diophantine Equation x^3+64=3y^2

丢番图方程x^3+64=3y^2的整数解至今未解决,利用奇偶数的性质、同余的性质等证明了丢番图方程x^3+64=3y^2仅有整数解(x,y)=(-4,0).

The integer solutions of the Diophantine equation x^3 ＋64= 3y^2 still remains unresolved. In this paper, we prove that the Diophantine Equation x^3＋64 = 3y^2 has only integer solution （x,y）= （-4,0） with the help of the natures of odd number, even number and congruence.