Prove, via induction or otherwise, that if $\displaystyle n\geq12,$ then n can be written as the sum of $\displaystyle 4's$ and $\displaystyle 5's$.

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- Jun 27th 2009, 06:54 PM #1

- Jun 27th 2009, 07:02 PM #2
$\displaystyle 12=4+4+4$

$\displaystyle 13=4+4+5$

$\displaystyle 14=4+5+5$

$\displaystyle 15=5+5+5$

$\displaystyle 16=4+4+4+4$

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Thus, if the number is a multiple of 4, it can be written as 4n

If the number is of the form 4n+1, it can be written as 4(n-1)+5

If the number is of the form 4n+2, it can be written as 4(n-2)+5*2

If the number is of the form 4n+3, it can be written as 4(n-3)+5*3.