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....
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| Format: | Article |
| Language: | zho |
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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 |
| _version_ | 1797235785956589568 |
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| author | YANGShichun(杨仕椿) TANGJiangang(汤建钢) |
| author_facet | YANGShichun(杨仕椿) TANGJiangang(汤建钢) |
| author_sort | YANGShichun(杨仕椿) |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T16:53:29Z |
| format | Article |
| id | doaj.art-437f8e4c221c4dd2945c03c465949a6f |
| institution | Directory Open Access Journal |
| issn | 1008-9497 |
| language | zho |
| last_indexed | 2024-04-24T16:53:29Z |
| publishDate | 2016-11-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj.art-437f8e4c221c4dd2945c03c465949a6f2024-03-29T01:58:36ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972016-11-0143667667810.3785/j.issn.1008-9497.2016.06.009Rational points on a class of super elliptic curve(一类超椭圆曲线上的有理点)YANGShichun(杨仕椿)0https://orcid.org/0000-0001-5692-7479TANGJiangang(汤建钢)1https://orcid.org/0000-0001-7662-0394 1.Department of Mathematics and Finance, Aba Teachers University, Wenchuan 623000, Sichuan Province, China( 1.阿坝师范学院数学与财经系，四川 汶川 623000) 2.College of Mathematics and Statistics, Yili Normal University, Yinning 835000, the Xinjiang Uygur Autonomous Region, China( 2.伊犁师范学院数学与统计学院，新疆 伊宁 835000)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.https://doi.org/10.3785/j.issn.1008-9497.2016.06.009有理点超椭圆曲线广义fermat方程 |
| spellingShingle | YANGShichun(杨仕椿) TANGJiangang(汤建钢) Rational points on a class of super elliptic curve(一类超椭圆曲线上的有理点) Zhejiang Daxue xuebao. Lixue ban 有理点 超椭圆曲线 广义fermat方程 |
| title | Rational points on a class of super elliptic curve(一类超椭圆曲线上的有理点) |
| title_full | Rational points on a class of super elliptic curve(一类超椭圆曲线上的有理点) |
| title_fullStr | Rational points on a class of super elliptic curve(一类超椭圆曲线上的有理点) |
| title_full_unstemmed | Rational points on a class of super elliptic curve(一类超椭圆曲线上的有理点) |
| title_short | Rational points on a class of super elliptic curve(一类超椭圆曲线上的有理点) |
| title_sort | rational points on a class of super elliptic curve 一类超椭圆曲线上的有理点 |
| topic | 有理点 超椭圆曲线 广义fermat方程 |
| url | https://doi.org/10.3785/j.issn.1008-9497.2016.06.009 |
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