Re: sqrt(Phi(n,b)) for n>2 and b>1
- --- In firstname.lastname@example.org,
"djbroadhurst" <d.broadhurst@...> wrote:
> This is the best that I could do, by way of an heuristic argumentThere was an error in Part (6), giving an upper bound
> that the probability of another (n,b) pair is less than 1/10^6.
for the probability of a solution with n > 100, sorry.
Here I correct it, with no change to the conclusion:
> 6) For n > 6 we know from[here I should have computed:]
> that eulerphi(n) > sqrt(n).
> Hence I estimate the probability of a solution
> with n > 100 as less than
[with the same conclusion:]
> which is far less than the estimate 2/10^7, in Part (4).David
> 7) In conclusion, I believe that there is a probability
> of less than 1/10^6 for finding a second integer pair (n,b),
> with n>2 and b>1, such that sqrt(Phi(n,b)) is an integer.
- We have written up (some of) our findings:
Kevin and David