# Discrete Mathematics Stamp problem [closed]

I am very confused on how to solve.

Use the Principle of Mathematical Induction to prove that every amount of postage of 18 cents or more can be formed using just 4-cent and 7-cent stamps.

• Do you have to use induction to prove? – Edward Jiang Apr 15 '16 at 3:03
• Yes, this must be proved by Mathematical Induction. – Bean Apr 15 '16 at 3:04
• Have you tried looking at some of these similar questions? – JMoravitz Apr 15 '16 at 3:08

You can create the first four in the following way:

$18 = 2\cdot 7 + 1 \cdot 4$

$19 = 1\cdot 7 + 3 \cdot 4$

$20 = 0\cdot 7 + 5 \cdot 4$

$21 = 3\cdot 7 + 0 \cdot 4$

Now assume that you can create all values $18, 19 , 20, 21, \cdots , k$.

Then you can create $k+1$ as $(k-3) + 1\cdot 4$. Hence, we are done by induction.