Rational points on a class of super elliptic curve(一类超椭圆曲线上的有理点)
设p为素数,r≥0是整数.利用广义Fermat方程的深刻结论证明了:若3 ≤ q<100,q≠ 31,则当p ≥ 5 时,超椭圆曲线yp = x(x+qr)上仅有平凡的有理点y = 0;当q = 5,11,23,29,41,47,59,83时,给出了该超椭圆曲线所有的有理点(x,y).特别地,当q = 3且r = 1时,证明了超椭圆曲线yp = x(x+3)仅在p = 2时有非平凡的有理点(x,y),并给出了此时所有的非平凡有理点....
Main Authors: | , |
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Format: | Article |
Language: | zho |
Published: |
Zhejiang University Press
2016-11-01
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Series: | Zhejiang Daxue xuebao. Lixue ban |
Subjects: | |
Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2016.06.009 |