by Kurt » Mon Apr 09, 2007 10:08 pm
Let [unparseable or potentially dangerous latex formula]
Then [unparseable or potentially dangerous latex formula][unparseable or potentially dangerous latex formula][unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
Since [unparseable or potentially dangerous latex formula] are powers of 3 themselves, then for some [unparseable or potentially dangerous latex formula], so [unparseable or potentially dangerous latex formula]
Using the second condition, we get:
[unparseable or potentially dangerous latex formula], or, rewriting and using the geometric sum formula:
[unparseable or potentially dangerous latex formula]. After seeing that, with such huge numbers, the 1's are going to barely matter at all:
[unparseable or potentially dangerous latex formula] (approximately).
Rewriting using [unparseable or potentially dangerous latex formula], or:
[unparseable or potentially dangerous latex formula] (again, approximately).
So we have as integer problems:
[unparseable or potentially dangerous latex formula]
Since [unparseable or potentially dangerous latex formula],
[unparseable or potentially dangerous latex formula]
or [unparseable or potentially dangerous latex formula] (as possible integer solutions):
But if [unparseable or potentially dangerous latex formula].
So [unparseable or potentially dangerous latex formula]:
And so [unparseable or potentially dangerous latex formula]
And thus [unparseable or potentially dangerous latex formula]