Hello all,

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

$\displaystyle

\phi(30)=\pi(30)-\pi(\sqrt30)+1

$

Now, I must show that

$\displaystyle

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

$

$\displaystyle 105=3*5*7$ has no factor of 2, so 105 has no factors in common with any of the primes greater than $\displaystyle \sqrt105$ 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.