The Integral Points on the Elliptic Curve y^2=7qx(x^2+128)
Authors: 
Fei Wan, Jianhong Zhao, Jihe WangAuthors Info & Claims
Fei Wan, Jianhong Zhao, Jihe WangAuthors Info & ClaimsPages 91 - 94
Abstract
The positive integer points of elliptic curves are very important in the theory of numbers and arithmetic algebra; it has a wide range of applications in cryptography and other fields.
The main purpose of this paper is to apply elementary methods, the properties of congruence and Legendre symbols, to study the elliptic curve <Formula format="inline"><TexMath><?TeX ${y}^2 = 7qx( {{x}^2 + 128} )$ ?></TexMath><File name="a00--inline2" type="gif"/></Formula> and proved that the elliptic curve has at most three integer points when <Formula format="inline"><TexMath><?TeX $q \equiv 5( {{\rm{mod}}8} )$ ?></TexMath><File name="a00--inline3" type="gif"/></Formula> is an odd prime number.
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Index Terms
- The Integral Points on the Elliptic Curve y^2=7qx(x^2+128)
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Published In
November 2023
327 pages
ISBN:9798400716973
DOI:10.1145/3653724
Copyright © 2023 ACM.
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Published: 19 June 2024
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ICMML 2023
ICMML 2023: International Conference on Mathematics and Machine Learning
November 24 - 26, 2023
Nanjing, China
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