Results 1 to 2 of 2

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 $\displaystyle n>=1$, if n is not prime, then neither is $\displaystyle 2^n-1$.

    How would I go about figuring this out? Is there a forumula or do I just plug numbers in?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Nov 2008

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

    Let $\displaystyle n=pq$ be a positive integer with $\displaystyle p,q\geq 2$
    $\displaystyle 2^n-1=2^{pq}-1^q=(2^p)^q-1^q=(2^p-1)(\sum\limits_{k=0}^{q-1}2^k)$

    Hence $\displaystyle \forall n\geq 1\ \text{no}(n\ \text{prime})\Rightarrow\ \text{no}(2^n-1\ \text{prime})$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: Feb 21st 2011, 04:37 AM
  2. Limit statement; True or False
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Oct 14th 2010, 09:32 PM
  3. Is this statement true or false?
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Apr 23rd 2010, 11:55 PM
  4. Replies: 1
    Last Post: Jun 14th 2009, 02:29 PM
  5. Surjections and a true/false statement.
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: Dec 17th 2008, 04:43 AM

Search Tags

/mathhelpforum @mathhelpforum