The integral points on elliptic curves $y^2=x^3+(36n^2 -9)x-2(36n^2-5)$

Title:

The integral points on elliptic curves $y^2=x^3+(36n^2 -9)x-2(36n^2-5)$

Creator:

Yang, Hai and Fu, Ruiqin

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:63bfbe71-84fa-42b0-adb4-c965bbb2b081
uuid:63bfbe71-84fa-42b0-adb4-c965bbb2b081

Subject:

elliptic curve, integral point; quadratic, and diophantine equation

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $n$ be a positive odd integer. In this paper, combining some properties of quadratic and quartic diophantine equations with elementary analysis, we prove that if $n>1$ and both $6n^2-1$ and $12n^2+1$ are odd primes, then the general elliptic curve $y^2=x^3+(36n^2 -9)x-2(36n^2-5)$ has only the integral point $(x, y)=(2, 0)$. By this result we can get that the above elliptic curve has only the trivial integral point for $n=3, 13, 17$ etc. Thus it can be seen that the elliptic curve $y^2=x^3+27x-62$ really is an unusual elliptic curve which has large integral points.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

375-383

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:2

Harvested from:

CDK

Metadata only:

false