Prove that any integer greater than or equal to $7$ can be written as a sum of two relatively prime integers, both greater than $1$.

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Prove that any integer greater than or equal to $7$ can be written as a sum of two relatively prime integers, both greater than $1$.For example, $22$ and $15$ are relatively prime, and thus $37 = 22+15$ represents the number $37$ in the desired way

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If $n=2k+1$ then $k,k+1$ are relatively prime.

If $n=4k$ then $2k-1,2k+1$ are relatively prime.

If $n=4k+2$ then $2k-1,2k+3$ are relatively prime.