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Math Help - proof by induction 5^n-1 is divisible by 4

  1. #1
    Member Jskid's Avatar
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    proof by induction 5^n-1 is divisible by 4

    Use mathematical induction to prove that the assertion is true for n\ge 1. 5^n-1 is divisible by 4.

    basis n_{o}=1 then 5^1-1=4 is divisible by 4.

    IH let 1\le l<k and assume 5^l-1 is divisible by 4.

    Induction Step
    5^{k}-1=(5)5^{k-1}-1
    Since 5^{k-1}-1 is divisble by 4 (by the induction hypothesis) then (5)5^{k-1}-1 is also divisible by 4

    Is this right?
    What is wrong with the latex
    Last edited by CaptainBlack; November 28th 2011 at 06:38 PM. Reason: fix LaTeX
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  2. #2
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    Re: proof by induction 5^n-1 is divisible by 4

    The induction step should have n = k+1
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  3. #3
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    Re: proof by induction 5^n-1 is divisible by 4

    IH let 1\le l<k and assume 5^l-1 is divisible by 4.
    If this is a proof by induction you need to go a step at a time, not prove it for all numbers at once.

    I'd say this. "Assume 4 |(5^k-1). We want to show 4|( 5^k^+^1-1)."

    Since 5^{k-1}-1 is divisble by 4 (by the induction hypothesis) then (5)5^{k-1}-1 is also divisible by 4
    Not quite, no. You have the formula wrong, and you need to show your work; how do you know 4 divides 5^k^+^1-1 for certain?
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