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

Abstract

Let p = 8k + 5, q = 8k + 3 be the twin prime pair for some nonnegative integer k. Assume that $$\\left({{5 \\over p}} \\right) = - 1$$(5p)=−1 or $$\\left({{7 \\over q}} \\right) = - 1$$(7q)=−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).