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riddles >> putnam exam (pure math) >> Coprimality of Two Randomly Chosen Integers
(Message started by: william wu on Aug 21st, 2003, 2:17pm)

Title: Coprimality of Two Randomly Chosen Integers
Post by william wu on Aug 21st, 2003, 2:17pm
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.

Title: Re: Coprimality of Two Randomly Chosen Integers
Post by SWF on Aug 21st, 2003, 6:23pm
What a coincidence! Just a few minutes ago I used that in solution to Random Line Segment in Square (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1049132168) riddle. However I left out the details to keep my post from being too long.

Title: Re: Coprimality of Two Randomly Chosen Integers
Post by TenaliRaman on Aug 22nd, 2003, 11:56am
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.



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