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

Question

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

Answer 1

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.