关于不定方程x^2+4~n=y^(15)(n=1,2,3)的整数解

The Solution on Diophantine Equation x^2+4~n=y^(15)(n=1,2,3)

不定方程整数解的问题是数论方面的一个重要问题。利用代数数论和同余理论的方法,研究不定方程x^2+4~n=y^(15)(x,y∈Z)的整数解问题,并证明了不定方程x^2+4~n=y^(15)(n=1,2,3)无整数解。

The integer solution of Diophantine equation is an important problem of the number theory, the problem of integer so-lution to the Diophantine equation x^2＋4^n=y^15（x,y∈Z） is discussed by using the methods of algebraic number theory and congruence theoryyand the Diophantine equation x^2＋4^n=^y15（n=1,2,3） which has no integer solution is proved.