Integral points on the elliptic curve y(2) = x(3)+27x-62

Abstract

We give a new proof that the elliptic curve y(2) = x(3) + 27x - 62 has only the integral points (x, y) = (2, 0) and (x, y) = (28,844,402, +/- 15,491,585,540) using elementary number theory methods and some properties of generalized Fibonacci and Lucas sequences.