Prove by strong induction on n that, for every integer n ≥ 4, it is possible to make n dollars using only two- and five-dollar bills. (That is, prove that any integer n ≥ 4 can be written as n = 2a +...

Prove by strong induction on n that, for every integer n ≥ 4, it is possible to make n dollars using only two- and five-dollar bills. (That is, prove that any integer n ≥ 4 can be written as n = 2a + 5b for some integer a ≥ 0 and some integer b ≥ 0.)