Guan, Xungui Integral points on the elliptic curve \(y^2 = x(x - p)(x - q)\). II. (Chinese. English summary) Zbl 1424.11074 J. Anhui Univ., Nat. Sci. 42, No. 2, 41-46 (2018). Summary: Let \(p, q\) be odd primes and \(m > 1\) be positive odd number with \(q - p = 2^m\), \(q \equiv 11\pmod{16}\). In this paper, the author proves that if \(m = 3\), then the elliptic curve \(y^2 = x(x - p)(x - q)\) \((x > q)\) has no integral point \((x, y)\). In addition, all integral points of the elliptic curve were given when \((p, q) = (11, 139)\). MSC: 11D25 Cubic and quartic Diophantine equations 11G05 Elliptic curves over global fields Keywords:elliptic curve; integral point; Diophantine equation; elementary method PDFBibTeX XMLCite \textit{X. Guan}, J. Anhui Univ., Nat. Sci. 42, No. 2, 41--46 (2018; Zbl 1424.11074) Full Text: DOI