3 Dec
2006
3 Dec
'06
3:34 p.m.
On Sunday 03 December 2006 18:35, Daniel Asimov wrote:
Let f(N) be the probability that 4 random integers i,j,k,m in the range 1 <= i,j,k,m <= N satisfy
gcd(i,j) = gcd(k,m) .
Find the limit of f(N) as N -> oo.
[The question that follows contains an implicit mild hint, so I'm inserting some blank lines. If you want to solve Daniel's problem without any clues at all, stop reading now; otherwise, scroll down as needed.] Question: is there a (sane) solution that gets to the correct answer without any instances of pi^2 and pi^4 along the way? -- g