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Math Help - Eulers totient function and exponentials

  1. #1
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    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?
    Last edited by dnftp; March 13th 2013 at 01:50 PM.
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  2. #2
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    Re: Eulers totient function and exponentials

    You need to factorise 1125.
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  3. #3
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    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.
    Last edited by dnftp; March 13th 2013 at 03:23 PM.
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  4. #4
    Super Member ILikeSerena's Avatar
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    Re: Eulers totient function and exponentials

    Hi dnftp!

    Quote Originally Posted by dnftp View Post
    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.

    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.
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