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Prove that any natural number greater than or equal to 12 is the sum of two composite numbers.

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    $\begingroup$ What have you tried so far? How would you approach this problem? $\endgroup$ Feb 22, 2019 at 5:29
  • $\begingroup$ What are your thoughts? Where did this problem come from? Why $12$? $\endgroup$
    – Somos
    Feb 22, 2019 at 5:30

1 Answer 1

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If $n$ is even, then $n$ is the sum of $4$, which is composite, and $n-4$, which is even (a multiple of 2), hence composite, provided $n>6$.

If $n$ is odd, then $n$ is the sum of $9$, which is composite, and $n-9$, which is even (a multiple of 2), hence composite, provided $n>11.$

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