----- Original Message ---- From: Eugene Salamin <gene_salamin@yahoo.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Monday, December 4, 2006 7:57:46 AM Subject: Re: [math-fun] Now for something completely different The same reasoning used for the original problem applies more generally. The probability that gcd(i[1],...,i[n]) = gcd(j[1],...,j[n]) is zeta(2n)/zeta(n)^2. It seems strange that for n even the answer is rational, while for n odd the result is of unknown character, presumably transcendental. Gene Further results: The probability that a quantity k of r-tuples of random integers all have the same gcd is zeta(kr)/zeta(r)^k. The probability the gcd of an r-tuple of random integers divides the gcd of an n-tuple of random integers is zeta(n+r)/zeta(n). I wonder if it's possible to find relations between different patterns of this kind, that lead to a formula connecting zeta functions of odd argument to each other or to pi. Is it known if odd zeta's are algebraic or transcendental in Q(pi)? Gene ____________________________________________________________________________________ Need a quick answer? Get one in minutes from people who know. Ask your question on www.Answers.yahoo.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun ____________________________________________________________________________________ Do you Yahoo!? Everyone is raving about the all-new Yahoo! Mail beta. http://new.mail.yahoo.com