数学与计算机科学 |
|
|
|
|
一类超椭圆曲线上的有理点 |
杨仕椿1,2, 汤建钢2 |
1. 阿坝师范学院 数学与财经系, 四川 汶川 623000; 2. 伊犁师范学院 数学与统计学院, 新疆 伊宁 835000 |
|
Rational points on a class of super elliptic curve |
YANG Shichun1,2, TANG Jiangang2 |
1. Department of Mathematics and Finance, Aba Teachers University, Wenchuan 623000, Sichuan Province, China; 2. College of Mathematics and Statistics, Yili Normal University, Yinning 835000, the Xinjiang Uygur Autonomous Region, China |
[1] GUY R K. Unsolved Problem in Number Theory[M]. 3rd ed. New York:Springer-Verlag,2004:4. [2] ERDÖS P, SELFRIDGE J L. The product of consecutive integers is never a power[J]. Illinois J Math,1975,19:292-301. [3] SANDER J W. Rational points on a class of superelliptic curves[J]. J London Math Soc,1999,59:422-434. [4] LAKHAL M, SANDER J M. Rational points on the superelliptic Erdos-Selfridge curve of fifth degree[J]. Mathematika:A Journal of Pure & Applied Mathematics, 2003,50(1/2):113-124. [5] SARADHA N, SHOREY T N. Almost perfect powers in arithmetic progression[J]. Acta Arith,2001,99:363-388. [6] SARADHA N, SHOREY T N. Almost squares and factorisations in consecutive integers[J]. Compositio Math,2003,138:113-124. [7] BENNETT M A. Products of consecutive integers[J]. Bull London Math Soc,2004,36:683-694. [8] DARON H, MCREL L. Winding quotients and some variants of Fermat's Last Theorem[J]. J Reine Angew Math,1997,490:81-100. [9] RIBET K A. On the equation ap+2bp+cp=0[J]. Acta Arith,1997,79:7-16. [10] SHEN Z Y, CAI T X. Rational points on three superellipric curves[J]. Bull Aust Math Soc,2012,85:105-113. [11] 沈忠燕,蔡天新.超椭圆曲线yk=x(x+2m)上的有理点[J].中国科学:数学,2012,42(6):645-650. SHEN Zhongyan, CAI Tianxin. Rational points on a superelliptic curve yk=x(x+2m)[J]. Sci Sin Math, 2012,42(6):645-650. [12] 任霄,沈忠燕.超椭圆曲线yk=x(x+1)(x+3)(x+4)上的有理点[J].数学的实践与认识,2015,45(23):291-299. REN Xiao, SHEN Zhongyan. Rational points on a superelliptic curve yk=x(x+1)(x+3)(x+4)[J]. Mathematics in Practice and Theory, 2015,45(23):291-299. [13] COHER H. Analytic and Modern Tools[M]//Number Theory. New York:Springer,2007:511-514. [14] COHER H. Tools and Diophantine Equations[M]//Number Theory. New York:Springer, 2007:373-376. |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|