关于不定方程x^3+64=21y^2

On Diophantine equation x^3+64=21y^2

利用递归数列、同余式和平方剩余几种初等方法,证明了不定方程x3+64=21y2仅有整数解(x,y)=(-4,0),(5,±3);给出了x3+64=21y2的全部整数解.

In this paper, the author has proved that the Diophantine equation x^3＋64=21y^2 has only an integer solution（x,y） = （ -4,0）, （5, ±3） and then gives all integer solution of x^3 ＋64 =21y^2 by using the elementary methods such as recursive sequence,congruent fomula and quadratic residue.