Prove that for each natural number n > 43, we can write
n = 6xn + 9yn + 20zn

for some nonnegative integers xn, yn, zn. then prove that 43 cannot be written in this
form.
(hint: write 44, 45, 46, 47, 48, and 49 in the given form. use induction to prove
that any larger number can be written in the given form.)