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2 order list of fractions, sum related problem

Source: Chile Finals 2006 L2 p1

October 3, 2022
algebraFraction

Problem Statement

Juana and Juan have to write each one an ordered list of fractions so that the two lists have the same number of fractions and that the difference between the sum of all the fractions from Juana's list and the sum of all fractions from Juan's list is greater than 123123. The fractions in Juana's list are 121,223,325,427,529,...\frac{1^2}{1}, \frac{2^2}{3},\frac{3^2}{5},\frac{4^2}{7},\frac{5^2}{9},... And the fractions in John's list are 123,225,327,429,5211,...\frac{1^2}{3}, \frac{2^2}{5},\frac{3^2}{7},\frac{4^2}{9},\frac{5^2}{11},... Find the least amount of fractions that each one must write to achieve the objective.
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