Hello All,

I am reading about the Euler Function phi(n), which my book defines counts the number of positive integers less then or equal to n, which are relatively prime. The book has a couple examples of how this works, but I do have some questions about a couple of the examples:

1. can be evaluated and proven correct. Can someone explain this?

2. Analyzing n:

If n is odd, then phi(2n)=phi(n)

If n is even, then phi(2n)=2*phi(n).

How can this be proven?

3. An n exists where phi(n)=phi(n+1)=phi(n+2). What is the n?

There are a few guidelines to this one, it says try taking phi(n)=2592. Then note that phi(2n)=phi(n) when n is odd. Then note that phi(p)=p-1 for a prime 'p'.

Any help is appreciated!