# Eulers totient function and exponentials

• Mar 13th 2013, 01:47 PM
dnftp
Eulers totient function and exponentials
I am trying to find all integer solutions to Euler's totient function $\phi(3^x \cdot 5^y) = 600$
From a theorem in my book $\phi(n) = n(1 - 1/p1)(1- 1/p1)$
I get $600 = 3^x\cdot5^y (2/3)(4/5)$
$3^x\cdot5^y = 1125$
Now I am stuck because I dont know how to solve this, any suggestions?
• Mar 13th 2013, 02:02 PM
a tutor
Re: Eulers totient function and exponentials
You need to factorise 1125.
• Mar 13th 2013, 03:17 PM
dnftp
Re: 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, 04:37 PM
ILikeSerena
Re: Eulers totient function and exponentials
Hi dnftp! :)

Quote:

Originally Posted by dnftp
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?

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.
I'm afraid that normal logarithms do not apply in number theory - they yield real numbers.
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.