The Integral Points on the Elliptic Curve y 2 = 7 qx(x 2 + 128)

Abstract

The positive integer points of elliptic curves are very important in the theory of numbers and arithmetic algebra; it has a wide range of applications in cryptography and other fields.The main purpose of this paper is to apply elementary methods, the properties of congruence and Legendre symbols, to study the elliptic curve y 2 = 7 qx(x 2 + 128)and proved that the elliptic curve has at most three integer points when q = 5(mod8) is an odd prime number.