Sorry It should be:

How can i show that

here are mobius function and Euler's phi function.

Printable View

- Jan 13th 2009, 05:43 AMpeteryellow
Sorry It should be:

How can i show that

here are mobius function and Euler's phi function. - Jan 13th 2009, 08:00 AMPaulRS

Remember that both, and are multiplicative, hence is multiplicative.

Now, recall the fact that if is a multiplicative arithmetic function then so is

From now on I will denote:

Now let's compute where is a prime number ( and s is greater than 0):

Now suppose is the prime descomposition of n.

Then

Now recall the fact that: and we are done - Jan 14th 2009, 04:04 AMpeteryellow
Thanks for veryyyyyyyy detalied reply. :-)