2015/019) Prove that there exists non negative integers a and b such that n=4a+5b for n >=12

we can specify from 12 to 15 as 4a+ 5b with a and b non -ve as below


12 = 3 * 4 + 0 * 5
13 = 2 * 4 + 1 * 5
14 = 1 * 4 + 2 * 5
15 = 0 * 4 + 3 * 5

Now for numbers > 15 if the number is
  4a then taken12 and add 4a-12
if 4a + 1 then 13 + 4(a-3)
if 4a + 2 then 14 + 4(a-3)
if 4a + 3 then 15 + 4(a-3)
as a >= 3 we have the result