丢番图方程x^(3)+1=2247y^(2)的整数解

Integer Solutions to the Diophantine Equation x^(3)+1=2247y^(2)

利用递归序列、同余、平方剩余、Pell方程的解的性质以及分类讨论等方法,证明了丢番图方程x^(3)+1=2247y^(2)仅有平凡整数解(x,y)=(-1,0).

The problem of integer solution of Diophantine equation x^(3)+1=2247y^(2) is studied in this paper.By means of recursive sequence,congruence,square residue,properties of solutions of Pell equation and classification discussion,it is proved that the Diophantine equation x^(3)+1=2247y^(2) has only trivial integer solution(x,y)=(-1,0).