The Jesus Christ Problem

[Ender]

The customer favorite in the Joe's Nicotine-Enhanced Candy Store is the Jesus Christ ice cream bar. Jesus Christ Ice Cream Bars come in either packs of 7 or packs of 9.

Q1. What is the maximum number of Jesus Christ Ice Cream Bars that one cannot buy?
Q2. How many integer amounts of Jesus Christ Ice Cream Bars can one not buy?
Q3. Generalize your answer to Q1 to any situation where Jesus Christ Ice Cream bars come in either packs of a or packs of b, where a and b are integers.

You don't have to wait until you get solutions to all three to post.

[rabbit]

1. infinite
2. infinite
3. yes

[Ender]

Incorrect.

[Nate]

You worded something wrong because the first two are infinite.

[Joe]

You worded something wrong because the first two are infinite.

Or he just said that at least one of them was incorrect, that being 3. It doesn't even make sense.

[leet_muffin]

1. 47?

[d&q]

The first two are infinite, one cannot buy an amount who's prime factorization does not include 9 or 7, which is an infinite set of numbers. I'm not sure about the third one though. Leet_muffin, how did you get 47?

[leet_muffin]

Try and add combinations of 9 and 7 to get 47. I couldn't. I didn't care to go any higher.

[d&q]

47 is a prime number, you shouldn't have bothered. 

[Edit]: Also, there is an infinitely high number of prime numbers if you care to know. I could look up the proof but I'm eating chicken right now and I'm too lazy.

[leet_muffin]

This has nothing to do with prime numbers...

[d&q]

How does it not?

Try and add combinations of 9 and 7 to get 47.

Ex: 9 + 9 +9 + 7 + 7

That is equivalent to 3^3 + 7^2. Any combinations you are adding will be equivalent to some form 3^x + 7^x. Which is called prime factorization.

[Edit]: I misread it, my mistake. 

[leet_muffin]

23 is a prime number. 7+7+9 = 23. I'm still not seeing how it involves prime numbers at all. Can you please explain?

[Ender]

1. 47?

You're right. Explain your answer though

Questions 2 and 3 still remain.

[leet_muffin]

Uh, any number (edit:)higher than 47 can be created through different combinations of 9 and 7.

I'll work on 2 and 3 later, I be going afk.

[Ender]

Uh, any number of 47 can be created through different combinations of 9 and 7.

I'll work on 2 and 3 later, I be going afk.

You need to elucidate. 47 is the maximum number that cannot be created by any combination of 9 and 7.

[Miamiandy]

I got all the answers.

1. The maximum number of bars that cannot be obtained is 47.
2. The number of interger amounts of bars that one cannot buy is 24.
3. If a and b are coprime positive integers then the maximum number of bars that cannot be bought is (a*b-a-b) bars.  Otherwise, an arbitrarily large number of bars cannot be bought.