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Math Help - Not prime number

  1. #1
    Super Member dhiab's Avatar
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    Not prime number

    Prouve that number is not prime number :
    (x is whole number no zero ) .
    Last edited by dhiab; June 6th 2009 at 11:34 AM.
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    is that the entire question? i feel there is something missing here...
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  3. #3
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    prove that this is not a prime.

    if x=1

    2 to the power of 2x +1 + 1 would equal

    2 to the power 3 +1

    8 + 1 = 9 which is not a prime
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    Hello, dhiab!

    Prove that N \;=\;2^{2n+1}+1 is not a prime number, for any positive integer n.

    N \;=\;2^{\text{odd power}} + 1 is always factorable.

    . . 2^{2n+1} + 1 \;=\;(2 + 1)\left(2^{2n} - 2^{2n-1} + 2^{2n-2} + \hdots + (\text{-}1)^{n+1}\right)


    Therefore, N is always a multiple of 3.

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  5. #5
    Super Member dhiab's Avatar
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    [quote=Soroban;326807]Hello, dhiab!


    N \;=\;2^{\text{odd power}} + 1 is always factorable.

    . . 2^{2n+1} + 1 \;=\;(2 + 1)\left(2^{2n} - 2^{2n-1} + 2^{2n-2} + \hdots + (\text{-}1)^{n+1}\right)


    Therefore, N is always a multiple of 3.

    [/quote
    Thank you for this resolution ?This my resolution (Theorem of induction)
    I prouve that : :
    - for : I have .
    -Now . I PROUVE FOR :
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    He3llo, again, dhiab!


    This is my resolution (induction)

    I prove that: . \forall x \in I^+,\;2^{2x+1} + 1 \:=\:3k

    For x = 1, I have: . 2^{2(1)+1} + 1 \:=\:2^3+1 \:=\:9 \:=\:3\cdot3

    Now: . 2^{2x+1} + 1 \:=\:3k\:\text{ for some integer }k.


    Prove for x+1:

    2^{2(x+1)+1}+1 \;=\;2^{2x+3} + 1 \;=\;4\cdot2^{2x+1} + 1 \;=\;3\cdot2^{2x+1} + \underbrace{(2^{2x+1}+1)}_{\text{This is }3k}
    Therefore: . 2^{2(x+1)} + 1 \;=\;3\cdot2^{2k+1} + 3k \;=\;3\bigg[2^{2k+1} + k\bigg]  \;=\;3m\:\text{ for some integer }m.

    Your inductive proof is correct!

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