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Integral points on elliptic curve \(y^2 = nx (x^2 + 16)\). (Chinese. English summary) Zbl 1438.11079

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
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