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#1 2013-10-08 12:40:13

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

phi

could someone give me a step by step solution. I figured out

was
which are odd numbers. I am not sure if i could do the same to this and divide it by 3.

Last edited by cooljackiec (2013-10-08 12:40:28)


I see you have graph paper.
You must be plotting something
lol

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#2 2013-10-08 12:59:36

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: phi

Hi

The answer is 2*3^99, like you thought it might be. For all primes p it is true that phi(p^n)=p^n-p^(n-1).


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#3 2013-10-08 15:40:44

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: phi

how would you prove that? by induction?


I see you have graph paper.
You must be plotting something
lol

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#4 2013-10-08 18:02:20

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: phi

Not exactly. I'd prove it using your idea. 1/p of the first p^n nunbers are not relatively prime to p^n and the rest is, so phi(p^n)=p^n-(1/p)*p^n=p^n-p^(n-1).


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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