| 摘要: |
| 不定方程整数解的问题是数论方面的一个重要分支,利用代数数论和同余的方法讨论不定方程x^2+64=4y^n(x,y∈Z),当n=7,11时整数解的问题,并证明了不定方程x^2+64=4y^n（n=7,11）无整数解. |
| 关键词: 不定方程 代数数论 整数解 |
| DOI： |
| 分类号: |
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| The Solution on Diophantine Equation x^2+64=4y^n(n=7,11) |
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SHANG Xu
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| Abstract: |
| The integer solution to Diophantine equation is an important branch of the number theory, the problem of integer solution to the Diophantine equation x^2+64=4y^n(x,y∈Z) is discussed by using the methods of algebraic number theory and congruence when n=7,11. and that the Diophantine equation x^2+64=4y^n(n=7,11) has no integer solution is proved. |
| Key words: Diophantine equation algebraic number theory integer solution |
