| 摘要: |
| 设Sm(n)是第m个n角数,给出当n-2为平方数时方程Sx(n)=Sy(3)的全部解的通式,并证明当n-2为非平方数时该方程有无穷多组正整数解 |
| 关键词: Diophantine方程 多角数 正整数解 |
| DOI： |
| 投稿时间：2003-11-21 |
| 基金项目:四川省教育厅重点科研基金资助项目([1999]127号). |
|
| On the Diophantine Equation Sx(n)=Sy(3) |
|
Yang Shichun
|
| (Aba Teacher's College, Dujiangyan, Sichuan, 611830, China) |
| Abstract: |
| Let Sm(n) denote the m-th n-gonal number.In this paper,the whole positive integer solutions of the Diophantine equation Sx(n)=Sy(3) are given when n>6 and n-2 is a square.We prove that if n-2 isn't a square,then the equation has infinitely many positive integer solutions. |
| Key words: Diophantine equation polygonal number positive integer solutions |
