Suppose p and q are unequal primes. Prove the following: a. pi(p)=p-1 b. pi(p^2)=p^2-p c. pi(p^n)=p^n-p^n-1 where n is a positive integer d. pi(pq)=pq-q-p+1 = (p-1)(q-1)
Last edited by teramaries; Jun 30th 2010 at 04:54 PM. Reason: mistake
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Originally Posted by teramaries Suppose p and q are unequal primes. Prove the following: a. pi(p)=p-1 b. pi(p^2)=p^2-p c. pi(p^n)=p^n-p^n-1 where n is a positive integer d. pi(pq)=pq-q-p+1 = (p-1)(q-1) Just list all the numbers less than or equal to the input of and count how many are divisible by the input.
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