On Aug 16, 2010, at 5:04 PM, Ian Kelly wrote:
On Mon, Aug 16, 2010 at 4:23 AM, Roald de Vries <downa...@gmail.com>
wrote:
I suspect that there exists a largest unpurchasable quantity iff at
least two of the pack quantities are relatively prime, but I have
made
no attempt to prove this.
That for sure is not correct; packs of 2, 4 and 7 do have a largest
unpurchasable quantity.
2 and 7 are relatively prime, so this example fits my hypothesis.
I now notice I misread your post (as 'iff the least two pack
quantities are relatively prime')
I'm pretty sure that if there's no common divisor for all three (or
more)
packages (except one), there is a largest unpurchasable quantity.
That is: ∀
i>1: ¬(i|a) ∨ ¬(i|b) ∨ ¬(i|c), where ¬(x|y) means "x is no
divider of y"
No. If you take the (2,4,7) example and add another pack size of 14,
it does not cause quantities that were previously purchasable to
become unpurchasable.
Then what is the common divisor of 2, 4, 7 and 14? Not 2 because ¬(2|
7), not anything higher than 2 because that's no divisor of 2.
Cheers, Roald
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