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pair (a,b) of positive integers so that (a + k)\(b+k) for all k \in {0,1,2,3,4}

Source: Rioplatense Olympiad 2014 level 3 P4

September 5, 2018

number theoryDivisorssets of integers

Problem Statement

A pair (a,b) of positive integers is Rioplatense if it is true that

b + k

is a multiple of

a + k

for all

k \in\{ 0 , 1 , 2 , 3 , 4 \}

. Prove that there is an infinite set

A

of positive integers such that for any two elements

a

and

b

A

, with

a < b

, the pair

(a,b)

is Rioplatense.