Integral points on the elliptic curve Epq: y2 = x3 + (pq − 12) x − 2(pq − 8)

Teng Cheng (), Qingzhong Ji () and Hourong Qin ()
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Teng Cheng: Nanjing University
Qingzhong Ji: Nanjing University
Hourong Qin: Nanjing University

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 2, 343-352

Abstract: Abstract Let p = 8k + 5, q = 8k + 3 be the twin prime pair for some nonnegative integer k. Assume that $$\left({{5 \over p}} \right) = - 1$$ ( 5 p ) = − 1 or $$\left({{7 \over q}} \right) = - 1$$ ( 7 q ) = − 1 . In this paper, we prove that the elliptic curve Epq: y2 = x3 + (pq − 12)x − 2(pq − 8) has unique integral point (2, 0).

Keywords: Elliptic curve; integral point; Fibonacci (Lucas) sequence (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13226-019-0329-4

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