Math Is Fun Forum

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

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)

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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).

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“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
The knowledge of some things as a function of age is a delta function.

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

Re: phi

how would you prove that? by induction?

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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).

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“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
The knowledge of some things as a function of age is a delta function.