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Math Help - Prime factors

  1. #1
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    Prime factors

    Hello!

    I've got a little problem with the following assignment. I would be very grateful if anyone could at least give me some hint on how to do it.

    There are given different odd prime numbers and . Prove that number has at least 3 different prime factors.

    Thank you very much!
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  2. #2
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    Quote Originally Posted by PaulinaAnna View Post
    Hello!

    I've got a little problem with the following assignment. I would be very grateful if anyone could at least give me some hint on how to do it.

    There are given different odd prime numbers and . Prove that number has at least 3 different prime factors.

    Thank you very much!
    Maybe this?

    Mersenne prime - Wikipedia, the free encyclopedia (subheading Generalization)

    By the way I've marked this thread to be moved to the Number Theory subforum.
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  3. #3
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    Let m and n be positive integers, if m|n, then 2^m-1|2^n-1.
    Also, for any positive integers m and n , if (m,n)=1 , then (2^n-1,2^m-1)=1.

    Apply these two lemmas in the same order they're written...
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  4. #4
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    Already solved

    Hey!

    Thank you guys very much.

    It's already solved
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  5. #5
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    Question

    Hey, I'm wondering how did you solve this problem? I'm interested, I tried with Mersenne numbers, but I didn't manage to prove that this number has at least 3 prime divisors.
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  6. #6
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    Anyway, I got it. It was quite easy.
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  7. #7
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    Err... No. My question remains- I "solved" it in the wrong way, now I realised. How to prove this fact?
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