I am trying to find all integer solutions to Euler's totient function

From a theorem in my book

I get

Now I am stuck because I dont know how to solve this, any suggestions?

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- Mar 13th 2013, 02:47 PMdnftpEulers totient function and exponentials
I am trying to find all integer solutions to Euler's totient function

From a theorem in my book

I get

Now I am stuck because I dont know how to solve this, any suggestions? - Mar 13th 2013, 03:02 PMa tutorRe: Eulers totient function and exponentials
You need to factorise 1125.

- Mar 13th 2013, 04:17 PMdnftpRe: Eulers totient function and exponentials
Thank you,

When I find the prime factors and their exponents x and y, am I justified in saying that these are the only ones as prime factorization in unique?

Edit- Also if anyone could show how to solve using logarithms I would be interested in knowing. - Mar 13th 2013, 05:37 PMILikeSerenaRe: Eulers totient function and exponentials
Hi dnftp! :)

Yes. A prime factorization is unique.

So you get unique solutions for x and y.

Quote:

Edit- Also if anyone could show how to solve using logarithms I would be interested in knowing.

As such they are not useful.

There is such a thing as a*discrete logarithm*, but let's not go there.

They are even harder to calculate than a large-number-prime-factorization.