Guan, Xungui Integral points on the elliptic curve \(y^2 = x(x - p)( x - q)\). I. (Chinese. English summary) Zbl 1424.11075 Math. Pract. Theory 48, No. 4, 272-279 (2018). Summary: Let \(p, q\) be odd primes and \(m\) be positive odd number with \(p + 2^m = q\), \(p \equiv 3\pmod 4\). In this paper, we prove that if \(m = 1\) or \(3\), then the elliptic curve \(y^2 = x(x - p)(x - q)\) \((x > q)\) has at most one integral point \((x, y)\); if \(m \geq 5\), then the elliptic curve has at most two integral points \((x, y)\). Additionally, all integral points of the elliptic curve when \((p, q) = (71, 103)\) are given. MSC: 11D25 Cubic and quartic Diophantine equations 11G05 Elliptic curves over global fields Keywords:elliptic curve; integral point; Diophantine equation; upper bound PDFBibTeX XMLCite \textit{X. Guan}, Math. Pract. Theory 48, No. 4, 272--279 (2018; Zbl 1424.11075)