Rational points on elliptic curves and representations of rational numbers as the product of two rational factors

Abstract

In this paper I demonstrate that any pair (m, n) of non-zero and distinct rational numbers may have, at most, four representations as the product of two rational factors such that the sum of factors of m coincides with the sum of factors of n. In the second part of the paper I derive the properties of elliptic curves such that the cubic has rational roots that satisfy this property