关于不定方程x^3+27=7y^2

On the Diophantine equation x^3+27=7y^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+27=7y2仅有整数解(x,y)=(-3,0),(1,±2);给出了x3+27=7y2的全部整数解.

In this paper,the author has proved that the Diophantine equation x^3 ＋ 27 = 7y^2 has only an integer solution（x,y） = （ -3,0） ,（ 1, ±2） and then gives all integer solution of x^3 ＋27 =7y^3 by using the elementary methods such as recursive sequence, congruent fomula and quadratic residue