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# Number Theory : Proof Problem

Prove that every natural number greater than or equal to 12 is the sum of two composite numbers. This proof is eating my mind. Please solve!

Note by Swapnil Das
2 years, 10 months ago

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Consider $$(9,(n-9))$$ and $$(8,(n-8))$$. Of these two pairs, at least one pair must consist of two composite numbers, why?

- 2 years, 10 months ago

If you want a lengthy proof , try using Chicken McNugget Theorem on multiple pairs of numbers .

- 2 years, 10 months ago