Probability breaker prime number and matrix : contest open (no google genius please)

Omk · September 7th, 2006, 7:23 pm

THis one is quite a hard one :1-what is the probability that 2 intergers have no common diviser except 1 ( they are prime to one another, like 4 and 15).(hint : you have to use the function zeta (not sure of the name) to write the answer, ie f x = sum 1/k^x k from 1 to inf, x>1)Another one as hard as the one before :Proove that when you take a matrix of normal gaussian number of size n*n and you look at the repartition function of its eigenvalues, you obtain a semi circle.Good luck !

sevvost · September 7th, 2006, 7:44 pm

Are there any exciting new developments since you had posted the first question less than a month ago?

Athletico · September 7th, 2006, 8:10 pm

QuoteOriginally posted by: Omk1-what is the probability that 2 intergers have no common diviser except 1 ( they are prime to one another, like 4 and 15).Gamma: Exploring Euler's Constant includes a very nice solution to this problem.