The Integral Points on Elliptic y2 = (x − 6)(x2 + 6x + 7). Issue 4 (June 2019)

• Record Type: Journal Article
• Authors: Zhao, Jianhong; Wei, Li; Fei, Wan
• Is Part Of: Journal of physics. Volume 1213:Issue 4(2019)
• Publication Date: 2019-06
• Subjects: Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/1213/4/042002
• Languages: English
• ISSNs: 1742-6588

Abstract

Abstract: In this paper, we studied the elliptic curve y 2 = ( x – a )( x 2 + ax + r ), a, r ∈ Z + in the case of a = 6, r = 7 which has no relevant conclusions up to now. And we obtained the conclusion of the integer points on Elliptic y 2 = ( x – 6)( x 2 + 6 x + 7 ), elliptic curve in title has only one integer point ( x, y ) = (6, 0) were proved with the help of the elementary methods such as congruence and Legendre symbol.