# mathematical induction

• April 13th 2009, 04:53 PM
relyt
mathematical induction
Show that any amount of postage of at least 12 cents can be made using 3 cent and 7 cent stamps?

I tried a couple of numbers of 12 and greater:

P(12) is true. 12 = 3 + 3 + 3 + 3.
P(13) is true. 13 = 7 + 3 + 3.
P(14) is true. 14 = 7 + 7.
P(15) is true. 15 = 3 + 3 + 3 + 3 + 3.
P(16) is true. 16 = 3 + 3 + 3 + 7
P(17) is true. 17 = 7 + 7 + 3
P(18) is true. 18 = 3 + 3 + 3 + 3 + 3 +3
P(19) is true. 19 = 3 + 3 + 3 + 7 + 3

??

Any help would be appreciated
• April 13th 2009, 05:00 PM
Mush
Quote:

Originally Posted by relyt
Show that any amount of postage of at least 12 cents can be made using 3 cent and 7 cent stamps?

I tried a couple of numbers of 12 and greater:

P(12) is true. 12 = 3 + 3 + 3 + 3.
P(13) is true. 13 = 7 + 3 + 3.
P(14) is true. 14 = 7 + 7.
P(15) is true. 15 = 3 + 3 + 3 + 3 + 3.
P(16) is true. 16 = 3 + 3 + 3 + 7
P(17) is true. 17 = 7 + 7 + 3
P(18) is true. 18 = 3 + 3 + 3 + 3 + 3 +3
P(19) is true. 19 = 3 + 3 + 3 + 7 + 3

and I can see that you can form postage of x + 1 by using postage of x - 3 plus an additional 3 cent stamp....but how do I show this to solve the problem?

Any help would be appreciated

You're trying to prove that any integer, p, greater than 11 can be written as $p = 3n+7m$, where n and m are natural numbers.
• April 13th 2009, 05:29 PM
relyt
I'm lost I guess...back to the books :(

Ugh...I'm really struggling with this one. Any additional help would be appreciated