关于不定方程x^2+4096=y^3的解

On Diophantine Equation x^2+4 096=y^3

丢番图方程是数论中一个重要组成部分,它不仅自身发展迅速,而且研究成果被广泛地应用于其他理学学科领域。利用数论中同余的性质,研究丢番图方程x2+4 096=y3(其中x≡1(mod 2),x,y∈Z)的解的情况。用代数数论的方法,证明了该方程无整数解。

Diophantine equation is a very important branch in number theory,which develop rapidly,and is widely used in the development of other subjects.By using the properties of congruence in number theory,the Diophantine equation x2＋4 096=y3（x≡1（mod 2）,x,y∈z） is studied and proved that the diophantine equation x2＋4 096=y3 has no integer solution.