Can someone please help me with this proof.

Find all n such that phi(n) = n/3.

Any help is much appreciated.

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- May 12th 2009, 02:54 AMjp3105Euler Phi-Function
Can someone please help me with this proof.

Find all n such that phi(n) = n/3.

Any help is much appreciated. - May 12th 2009, 03:44 AMPaulRS
To start with, note that, since is either 1 or an even number, n must be even.

Remember that: (the products go over the prime numbers p dividing n)

Thus:

Now since 3 is a prime number, and it follows that 3 is one of the prime factors in the product. Thus: and 2|n thus: and this is only possible if there are no other prime factors.

Thus: with

And conversely this number satisfies the condition for any