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, 2015

Number theory Difficulty 5.0 AIME, harder Prove it United Kingdom

Two integers are $\emph{relatively}$ prime} if their highest common factor is $1$ . I choose six different integers between $90$ and $99$ inclusive. (a) Prove that two of my chosen integers are relatively prime. (b) Is it also true that two are $\emph{not}$ relatively prime?

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