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Smallest number that belongs

Source: Brazilian Math Olympiad - University Level - Galois-Noether 2018 #5

November 24, 2019
SetsalgebraBrazilian Math OlympiadBrazilminimum valueminimization

Problem Statement

Consider the set A={j4+100j∣j=1,2,3,..}A = \left\{\frac{j}{4}+\frac{100}{j}|j=1,2,3,..\right\} What is the smallest number that belongs to the A A set?
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