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Let $n>30$. Then prove there exists a natural number $1$(n,m)=1$ and $m$ is not prime.

$(m,n)$ denotes the greatest common divisor of $m$ and $n$. Thanks

  • 0
    Why are you requiring $n\gt30$?2012-11-27
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    this is not true for $n<30$2012-11-27
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    @elham It is definitely true, as stated, for $n<30$.2012-11-27
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    Perhaps you intended to include the condition $m\lt n$ and forgot?2012-11-27
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    @joriki Ah, that's probably it.2012-11-27
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    Note, as stated, $m=1$ works for all $n$. $1$ is a natural number, $1$ is not prime, and $(1,n)=1$ for all $n$.2012-11-27
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    I took the liberty to make the inequality $1 strict, to avoid trivial answers.2012-11-27

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