Here is another question that I got stuck with. Please see attachment. I typed the question in " Microsoft word" . If you can't load the attachment , please do let me know.
Here is another question that I got stuck with. Please see attachment. I typed the question in " Microsoft word" . If you can't load the attachment , please do let me know.
Thank you very much.
Did you consider using the Mobius inversion formula?
If is multiplicative then,
Now, is multiplicative function
And (the Mobius mu function) is also multiplicative.
Thus, is also multiplicative.
Thus, is multiplicative (because of the summation theorem).
Last edited by ThePerfectHacker; December 27th 2006 at 12:22 PM.
Thank you very much for your reply. I have never learnt Mobius inversion forumla. I will go through your prove. If I don't understand it, I will come back to you.
Can you show me the other way ( not by mobius inversion forumla) to prove this question? I don't really get your prove because I dont' quite understand the mobius inversion formula. Thank you very much for your help.
Can you show me the other way ( not by mobius inversion forumla) to prove this question? I don't really get your prove because I dont' quite understand the mobius inversion formula. Thank you very much for your help.
I just looked up the proof in my number theory book and they prove it the same way I did. Thus, perhaps this is the standard way.