Thread: 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

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 , where n and m are natural numbers.

I'm lost I guess...back to the books

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