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Math Help - Primes

  1. #1
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    Primes

    Given are distinct odd primes a,b. Show that  2^{ab}-1 has at least 3 distinct prime divisors.

    No idea how to approach this one, so I would gladly use a hint and try to get at it myself. Thank you in advance.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    In my opinion you should try the Chinese remainder theorem... (But maybe I wrong here)

    Or by using Euler's theorem (Euler's theorem - Wikipedia, the free encyclopedia), prove that for every combination of ab(under conditions) exist n such that ab=\phi(n)=p_1\cdot p_2 \cdot p_3 \cdot m, when p_1,p_2,p_3 your primes...

    Interesting...
    Last edited by Also sprach Zarathustra; October 19th 2010 at 03:28 PM.
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  3. #3
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    Lowest would be 2^(3*5)-1 = 32767: 7,31,151
    But beyond my humble abilities to "show".
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