Proving Every Int. ≥ 12 Is a Combination of 4m + 5n

[hocuspocus102]

Homework Statement

Prove that every integer greater than or equal to 12 can be written as a combination of 4m+5n where m and n are non-negative integers.

Homework Equations

The Attempt at a Solution

I know I have to use induction but I don't really know how to go about doing it past showing that it works for the base case of n=12 where then a=3 and b=0.

 

[l'Hôpital]

Hint: 1 = 5 - 4