Is 2008! divisible by $\displaystyle 9^{400}$?
I figure this uses mods somewhere......can someone show me a nice place to start?
right, I think I getcha!
$\displaystyle \left[\frac{2008}{3} \right]+\left[ \frac{2008}{3^2} \right]+\left[ \frac{2008}{3^3}\right]+\left[ \frac{2008}{3^4} \right]+\left[ \frac{2008}{3^5} \right]+\left[ \frac{2008}{3^6} \right]+\left[ \frac{2008}{3^7} \right]+\left[ \frac{2008}{3^8} \right]+....$
$\displaystyle =669+223+74+24+8+2+0+....>800$
(Whose formula is this known as? Is it De pognac's?)
So it is possible to have 800 3's in the prime decomposition of 2008!
Thanks Moo
P.S: How do you get those really cool spoiler windows to appear?
Yes
Whew...I struggled with finding these threads :
http://www.mathhelpforum.com/math-he...orization.html
http://www.mathhelpforum.com/math-he...ation-2-a.html
They may give you further insight on the formula
I don't know the name(Whose formula is this known as? Is it De pognac's?)
But I looked for de Pognac and didn't find anything significant
With the [spoiler][/spoiler] tagsP.S: How do you get those really cool spoiler windows to appear?
okay, i'll read through those threads.
Meanwhile, I found out whose formula this is:
De Polignac's formula - Wikipedia, the free encyclopedia