Problem Solving

The function F is defined for all positive integers N by the following rule: F(N) is the number of positive integers each of which is less than N and has no positive factor in common with N other than 1. If P is any prime number the F(P)= what?

The answer is P-1...help?!

The best way to handle a problem like this, I think, is to do a quick example to understand the function F. F(8) = 4 {7,5,3,1}.

Therefore, pick any prime, say 11. F(11) = 10 {10, 9,8,7,6,5,4,3,2,1} which makes sense because the prime number, by definition, doesn't share any positive common factors with any other number.

So, F(P) = P-1 when P is a prime