Function f(n) gives number of pos. integers < n

[mcheytan]

Ok I have this one:

The function f(n) = the number of positive integers that are <n, and has no positive factor with n other than 1. (does this mean that the number is prime number???) If p=prime number, then what is f(p)=?

I guessed that the solution is f(p)=p-1
I do not know why I think this way, it is correct.
Is it because we have to exclude 1 as a number in the f(n) because it is not a prime number as f(n) is supposed to represent?

 

[skeeter]

Re: Function f(n)

two numbers with no common factors other than 1 are relatively prime.

if n = p, a positive prime, then there are p -1 positive integers less than p with no common factors (otherwise p would not be prime, would it?)

 

[mcheytan]

Oh yes, I think I am getting it!