| 丢番图方程a^x＋b^y=c^z的正整数解 |
| |
| 引用本文： | 陈进平. 丢番图方程a^x＋b^y=c^z的正整数解[J]. 海南大学学报(自然科学版), 2012, 30(4): 309-315 |
| |
| 作者姓名： | 陈进平 |
| |
| 作者单位： | 西华师范大学数学与信息学院,四川南充,637002 |
| |
| 基金项目： | 西华师范大学大学生科技创新基金项目 |
| |
| 摘 要： | 设m为正整数，且a=m^7-21m^5＋35m^3-7m，b=7m^6-35m^4＋21m^2-1，c=m^2＋1．本文同时利用2个代数数的线性型下界估计以及2个有理数方幂之差的p-adie值的下界估计的一些深入结果，证明了对正整数m≥2．4×10^9，丢番图方程a^x＋b^y=c^z仅有正整数解（x，y，z）=（2，2，7）．
|
| 关 键 词： | 丢番图方程 TERAI猜想 正整数解 对数线性型 p-adic标准值 |
Positive Integer of Diophantine Equation ax + by =cz |
| |
| CHEN Jin-ping. Positive Integer of Diophantine Equation ax + by =cz[J]. Natural Science Journal of Hainan University, 2012, 30(4): 309-315 |
| |
| Authors: | CHEN Jin-ping |
| |
| Affiliation: | CHEN Jin-ping ( College of Mathematics and Information, China West Normal University, Nanehong 637002, China) |
| |
| Abstract: | In our report, let m ∈n,a =m^7 -21m^5 ＋35m^3 -7m,b =7m^6 -35m^4 ＋21m^2 - 1 ,c =m^2 ＋ 1, A deep result of the lower bound for linear forms in two logarithms and the lower bound for the p-adic distance between two powers of rational numbers were used to prove that if m≥2. 4 x 109, the Diophantine equation a^x ＋ b^y = c^z has only one positive integer solution （x,y,z） = （2,2,7）. |
| |
| Keywords: | Diophantine equation Terai conjecture positive interger solution linear forms in two logarithms p-adic standard value |
| 本文献已被 维普 万方数据 等数据库收录！ |
|
