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Minimum and maximum value of \frac{a}{b}+\frac{c}{d}

Source: XIX Olimpíada Matemática Rioplatense (2010)

July 22, 2011

inequalitiesnumber theory unsolvednumber theory

Problem Statement

Find the minimum and maximum values of

S=\frac{a}{b}+\frac{c}{d}

where

a

b

c

d

are positive integers satisfying

a + c = 20202

and

b + d = 20200