Cut the question down to size by picking a value of p:
Suppose p=5
f(p) is defined as the number of positive integers less than p that do not have any prime factors in common with 5. Since no positive integer less than 5 is a multiple of 5, f(5) = 4 i.e. 5 - 1
A
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No of positive Integers
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reasoning is f(n)= all no. less then n and having no factors common with n
i.e if n=8 ; f(n)=1,3,5,7
if n=p ( a prime no.)= say 7
f(p)=1,2,3,4,5,6[tot=6] ( as none has common factor with7 and since its a prime no. it will not have any factor apart from 1 and the no. it self)
hence for all p's ; f(p)=p-1
i.e if n=8 ; f(n)=1,3,5,7
if n=p ( a prime no.)= say 7
f(p)=1,2,3,4,5,6[tot=6] ( as none has common factor with7 and since its a prime no. it will not have any factor apart from 1 and the no. it self)
hence for all p's ; f(p)=p-1
