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Math Help - Induction Proof

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    Induction Proof

    Prove that (5^2n) - 1 is a multiple of 8 for all natural numbers. (By induction)
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    Quote Originally Posted by bearej50 View Post
    Prove that (5^2n) - 1 is a multiple of 8 for all natural numbers. (By induction)
    .....Here is the main part
    Let 5^2k-1 is a multiple of 8
    so
    5^{2k}-1 =8 m [ m is any integer]

    5^2k = 8m+1

    For(k+1)

    5^{2(k+1)}-1

    =25*5^{2k}-1

     <br />
=25*(8m+1)-1<br />
    =25*8m+24

    =8(25m+3)
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    thank you!
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