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Thread: True or False Statement?

  1. #1
    Junior Member
    Aug 2007

    True or False Statement?

    If True explain show why and if false give a counterexameple.

    For All n>=1, if n is not prime, then neither is 2^n-1.

    How would I go about figuring this out? Is there a forumula or do I just plug numbers in?
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  2. #2
    Senior Member
    Nov 2008

    A useful formula: \forall a,b,n\in\mathbb{N},\ n\geq 2,\ a^n-b^n=(a-b)(a^{n-1}+a^{n-2}b+...+ab^{n-2}+b^{n-1})

    Let n=pq be a positive integer with p,q\geq 2

    Hence \forall n\geq 1\ \text{no}(n\ \text{prime})\Rightarrow\ \text{no}(2^n-1\ \text{prime})
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