Hello all,

I have a simple question for you. Using the fact that 30 is a product of all the primes less than \sqrt30, I have shown that

<br />
\phi(30)=\pi(30)-\pi(\sqrt30)+1<br />

Now, I must show that

<br />
(1/2)\phi(105)=\pi(105)-\pi(\sqrt105)+1<br />

105=3*5*7 has no factor of 2, so 105 has no factors in common with any of the primes greater than \sqrt105 but less than 105 (as with 30).

It also has no factors in common with the the composite numbers that are multiples of 2 and these primes. So, other than by listing, how would one show that there is an equal number of multiples of 2 and these primes (whose product is less than 105) and the number of these primes. That would complete my proof.

Hopefully that makes sense.

Thanks.