[math-fun] number theory puzzle about squarefree number density

If you pick a random uniform number n with 0<n<=N then the probability n will be squarefree goes to 6/pi^2=60.79% in the limit N-->infinity. You probably already knew that. Result by Euler. Kind of a very inefficient way to calculate pi. Now, which are somewhat harder: PUZZLE #1: what is the probability that both n and n-1 are squarefree? PUZZLE #2: what is the probability that at least one of {n,n-1} is squarefree? (Actually, if you solve one puzzle, I think you'll find it very easy to solve the other...) -- Warren D. Smith http://RangeVoting.org  <-- add your endorsement (by clicking "endorse" as 1st step)