Guo, Mengyuan; Gao, Li; Zheng, Lu Integral points on elliptic curve \(y^2 = nx (x^2 + 16)\). (Chinese. English summary) Zbl 1438.11079 J. Yunnan Minzu Univ., Nat. Sci. 28, No. 2, 135-137 (2019). Summary: Let \(n\) be a positive odd number, whose prime factors could be \(P_j \equiv 3, 7 \pmod 8\), \((j \in {\mathbb{Z}^+})\). It is proved that the elliptic curve \(y^2 = nx (x^2 + 16)\) has only two positive integer points except \((0, 0)\) by some properties of congruence and the Legendre symbol. MSC: 11D25 Cubic and quartic Diophantine equations 11G05 Elliptic curves over global fields Keywords:elliptic curve; integer points; odd prime; congruence; Legendre symbol PDFBibTeX XMLCite \textit{M. Guo} et al., J. Yunnan Minzu Univ., Nat. Sci. 28, No. 2, 135--137 (2019; Zbl 1438.11079) Full Text: DOI