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Keywords:
elliptic curve; integral point; Diophantine equation
elliptic curve; integral point; Diophantine equation
Summary:
The main purpose of this paper is to prove that the elliptic curve $E\colon y^2=x^3+27x-62$ has only the integral points $(x, y)=(2, 0)$ and $(28844402, \pm 154914585540)$, using elementary number theory methods and some known results on quadratic and quartic Diophantine equations.
References:
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