Prev: Terra incognita, Sacred ground, Mysterious territory.
Next: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
From: Henry on 4 May 2010 20:09
On 4 May, 23:33, Butch Malahide <fred.gal...(a)gmail.com> wrote:
> On May 4, 4:47 pm, Disc Magnet <discmag...(a)gmail.com> wrote:
>
> > Is it true that m divides the binomial coefficient C(mn, n)?
>
> > I couldn't find a counterexample, [. . .]
>
> How hard did you look? Did you try m = n = 3?

C(3*3,3) = 84 which is divisible by 3

except in MS Excel
where =MOD(COMBIN(3*3,3),3)
gives a peculiar -1.42109E-14
From: Butch Malahide on 4 May 2010 21:01
On May 4, 7:09 pm, Henry <s...(a)btinternet.com> wrote:
> On 4 May, 23:33, Butch Malahide <fred.gal...(a)gmail.com> wrote:
>
> > On May 4, 4:47 pm, Disc Magnet <discmag...(a)gmail.com> wrote:
>
> > > Is it true that m divides the binomial coefficient C(mn, n)?
>
> > > I couldn't find a counterexample, [. . .]
>
> > How hard did you look? Did you try m = n = 3?
>
> C(3*3,3) = 84 which is divisible by 3

Oh, right. Brain cells going even faster than I thought.
From: Rob Johnson on 4 May 2010 21:03
In article <e74f39fc-25f5-4683-8553-f4f954e859f5(a)s4g2000prh.googlegroups.com>,
Disc Magnet <discmagnet(a)gmail.com> wrote:
>Is it true that m divides the binomial coefficient C(mn, n)?
>
>I couldn't find a counterexample, neither could I prove it. Any help?

If n = 0 and m > 1, then m does not divide C(0,0) = 1. However,
notice that

C(mn,n)

= (mn)/n C(mn-1,n-1)

= m C(mn-1,n-1)

Therefore, as long as n > 0, m divides C(mn,n).

Rob Johnson <rob(a)trash.whim.org>
take out the trash before replying
to view any ASCII art, display article in a monospaced font
First  |  Prev  | 
Pages: 1 2
Prev: Terra incognita, Sacred ground, Mysterious territory.
Next: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv