不定方程x^2+1024=y^15整数解的研究

Integer Solution of the Diophantine Equation x^2+1024=y^15

在数论中,不定方程是一个重要的分支,大量学者对其进行了研究。基于代数数论和同余理论探讨了不定方程x^2+1024=y^15,x、y∈Z整数解的存在问题,并得出该不定方程x^2+1024=y^15,x、y∈Z没有整数解的结论。

In number theory,the Diophantine equation is an important branch which has drawn extensive research.In this paper,the integer solution to the Diophantine equation x^2+1024=y^15 is studied by applying the knowledge of algebraic number theory and congruence theory,and it is acquired that the Diophantine equation x^2+1024=y^15 has no integer solution.