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**DivideBy0** Exercise 2.9. Prove that if n ≥ 12 then n can be written as a sum of 4’s and 5’s. For example, 23 = 5 + 5 + 5 + 4 + 4 = 3 · 5 + 2 · 4. [Hint. In this case it will help to do the cases n = 12, 13, 14, and 15 separately. Then use induction to handle n ≥ 16.]

It's not too hard to provide cases for n = 12, 13, 14, 15, but the second bit is hard:

If n = 5a + 4b, then n + 1 = 5c + 4d?

Any tips on how to get started? I think I'm introducing too many variables, but I duno really :/