PS

Question

Can anyone solve this pls.?

kevincan · Answer

If p is a prime number, it has only two factors, p and 1. So, as any integer less than p will not have p as a factor f(p)= the number of postive integers less than p, i.e. p-1

lan583 · Answer

The answer is A. But can anyone tell me a clearer explanation on this. Thanks

kevincan · Answer

Ask yourself "What is f(11)?" In other words, how many postive integers less than 11 have no factor (other than 1) in common with 11?

If p is a prime number, say 11, then f(p) is the number of integers from 1 to p-1 (example from 1 to 10) for which the only factor common between n and p is 1.

We know that p has only two factors, 1 and p
Also, any integer n less than p is not divisible by p ---p is not a factor of n
Thus 1 is the only factor common between n and p

Thus f(p)= the number of integers from 1 to p-1 i.e. p-1

Is this a clearer explanation?

jaynayak · Answer

Clearly A.

Since P is a prime number, all the other numbers less than P has no common factors with P.

hence the F(p) = p-1

Futuristic · Answer

I chose B initially, thinking that we could not include 1 in the list of numbers. Clearly poor concentration at 12am. Agreed the answer is A

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