If anyone could shed some light on this problem, especially the second part to part a, I would be most grateful!

http://img217.imageshack.us/img217/921/48698386.jpg

Printable View

- February 22nd 2011, 05:58 PMLHSDivisibility of binomial coefficients, countability of N^k.
If anyone could shed some light on this problem, especially the second part to part a, I would be most grateful!

http://img217.imageshack.us/img217/921/48698386.jpg - February 22nd 2011, 07:25 PMtonio
- February 23rd 2011, 05:07 AMLHS
Sorry? I don't understand, can you not see the inbeded image?

If not, here it is

http://img217.imageshack.us/img217/921/48698386.jpg - February 23rd 2011, 05:39 AMtonio

I'm afraid somebody's hacked the MHF: all over the place appear those annoying frogs inside ice cubes, and

that's what I saw instead your embedded image.

Anyway, following the link above I get...a frog inside an ice cube again! I don't know what's going on.

Perhaps somebody hacked the imageshack site and now we've been infected...

Tonio - February 23rd 2011, 05:46 AMLHS
Haha.. right, ok, that certainly explains it! No worries!

- February 23rd 2011, 05:47 AMAckbeet
Here's the question:

(a) Let be a prime number. Prove that for any natural number such that the binomial coefficient is divisible by Hence prove that, for any positive integer the integer is divisible by

(b) Let with and let be given by

where is the th prime. Deduce from the Fundamental Theorem of Arithmetic that is injective and hence that is a countable set for each

[EDIT]: Both links and image are fine for me.