| 摘要: |
| 运用Gel'fond-Baker方法证明,在m ≥ 105r3时,丢番图方程ax+by=cz仅有正整数解(x,y,z)=(2,2,r).其中r和m为正偶数,(a,b,c)=(|V(m,r)|,|U(m,r)|,m2+1),V(m,r)+U(m,r)√-1=(m+√-1)r. |
| 关键词: 丢番图方程 Terai猜想 正整数解 Gel'fond-Baker方法 |
| DOI： |
| 投稿时间：2012-08-27 |
| 基金项目: |
|
| Solution of Pure Exponential Diophantine Equations ax+by=cz for Generalized Pythagorean Triplets |
|
CHEN Jin-ping
|
| (College of Mathematics and Information, China West Normal University, Nanchong, Sichuan, 637002, China) |
| Abstract: |
| Using the Gel'fond-Baker method, we prove that if m ≥ 105r3, then the Diophantine equation ax+by=cz has only one positive integer solution (x, y, z)=(2, 2, r).Let r and m be a positive even integer, (a, b, c)=(|V(m, r)|,|U(m, r)|, m2+1), V(m, r)+U(m, r)√-1=(m+√-1)r. |
| Key words: Diophantine equation Terai conjecture positive interger solution Gel'fond-Baker method |
