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

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