wu :: forums - Coprimality of Two Randomly Chosen Integers

wu :: forums « wu :: forums - Coprimality of Two Randomly Chosen Integers » Welcome, Guest. Please Login or Register. Apr 19^th, 2024, 2:20am
RIDDLES SITE WRITE MATH! Home Help Search Members Login Register

   wu :: forums
   riddles
   putnam exam (pure math) (Moderators: towr, SMQ, Eigenray, Icarus, Grimbal, william wu)
   Coprimality of Two Randomly Chosen Integers

« Previous topic | Next topic »

Pages: 1

Notify of replies

Send Topic

Author

Topic: Coprimality of Two Randomly Chosen Integers (Read 965 times)

william wu
wu::riddles Administrator

Gender:

Posts: 1291

Coprimality of Two Randomly Chosen Integers
« on: Aug 21^st, 2003, 2:17pm »

Quote

Modify

Show that

[prod]_{p in primes}(1 - p^-2) = 6[pi]^-2

Conclude that the probability two randomly chosen integers are coprime is 6[pi]^-2.

IP Logged

[ wu ] : http://wuriddles.com / http://forums.wuriddles.com

SWF
Uberpuzzler

Posts: 879

Re: Coprimality of Two Randomly Chosen Integers
« Reply #1 on: Aug 21^st, 2003, 6:23pm »

Quote

Modify

What a coincidence! Just a few minutes ago I used that in solution to Random Line Segment in Square riddle. However I left out the details to keep my post from being too long.

IP Logged

TenaliRaman
Uberpuzzler

I am no special. I am only passionately curious.

Gender: male

Posts: 1001

Re: Coprimality of Two Randomly Chosen Integers
« Reply #2 on: Aug 22^nd, 2003, 11:56am »

Quote

Modify

hey the second question's pretty neat!!!
it had me hooked up for the last 5 hours before it dawned on me that P(coprime)=1-P(not coprime) and the first result comes into play.

IP Logged

Self discovery comes when a man measures himself against an obstacle - Antoine de Saint Exupery

Pages: 1

Notify of replies

Send Topic


« Previous topic \| Next topic »