[Solved] The Toothfairy Problem

[Ender]

Show that 7^n - 1 is divisible by 6 for any positive integer n.

I'll post the solution on Wednesday.

[Rule]

Simple induction...  is this a homework assignment question?

[Sidoh]

[Rule]

You need to specify that you are assuming 7^k-1 is divisible by 6 for some k>=1, then you have shown the formula holds for all n>=1. 

A picky detail, but one that is notable in rigorous math courses.

[rabbit]

Done.

[Sidoh]

You need to specify that you are assuming 7^k-1 is divisible by 6 for some k>=1, then you have shown the formula holds for all n>=1. 

A picky detail, but one that is notable in rigorous math courses.

Oops, yeah.  I should have said "Assume 7^k-1 is divisible by 6 for some arbitrary integer greater than one, k," right?

[Ender]

Another way to do this, which does not require knowledge of modular arithmetic or number theory, is using the polynomial combinatorics whatever theorem:

[rabbit]

While that may not require knowledge of modular arithmetic and number theory, it does require either (A) set theory (I think) or (B) basic discrete concepts.

[Ender]

2 + 2 requires knowledge of set theory =p

but yeah it requires knowledge of basic combinatorics

[rabbit]

Which is Discrete, vis a vis same level as NT :P

[Ender]

Discrete math is much more common to high school math curricula* than number theory is, but yeah, there's no restriction to what math you can use in these problems.

* Grammar Policed on behalf of Sidoh's (pedantic) request

[Sidoh]

curriculae

You made that word up. :P

[rabbit]

Discrete math is much more common to high school math curricula* than number theory is, but yeah, there's no restriction to what math you can use in these problems.

* Grammar Policed on behalf of Sidoh's (pedantic) request

Hmmm....that means I can use my made up math!

[Sidoh]

* Grammar Policed on behalf of Sidoh's (pedantic) request

If it's truely pedantic, why did you go through the effort of fixing it?

[Ender]

I just wanted to use the word pedantic because I rarely get to use it and it's really fun to say.