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## Homework Statement

Prove that, in any set of n + 1 positive integers (n ≥ 1) chosen from the set {1, 2, . . . 2n}, it must be that two of them are relatively prime (i.e. have no common divisor except 1). ( Hint: two consecutive integers are relatively prime. Make boxes labelled by pairs of consecutive integers. ).

## Homework Equations

## The Attempt at a Solution

In boxes does it mean to write:

[1,2]

[2,3]

[3,4]

[4,5]

[5,6]

[6,7]...

and i don't understand how two consecutive integers are relatively prime.