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When $a$ is odd then $a=p+q$ where either $p$ is even or $q$ is even.

If $p$ is even then $q$ is odd and hence $p$ and $q$ are relatively prime to each other. Similarly, vice versa.

Therefore, $GCD(p,q)=1$

Hence, any integer $n≥7$ is the sum of two relatively prime integers.

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