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March 28, 2017

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Prove via Mathematical Induction that

(7*n) - 1 is divisible by 6.

I have that it is divisble when n=1, but not n=2 and so on. How should I write the inductive proofs?

  • Calculus - ,

    It's obviously not true.

    7*2-1 = 13 which is not divisible by 6

    I think you mean 7^n-1 is divisible by 6

    when n=1, 7^1-1 = 7-1 = 6 is divisible by 6
    assume for n=k
    when n=k+1,
    7^(k+1)-1 = 7*7^k - 1
    = 7*7^k -7 + 6
    = 7(7^k-1) + 6
    but, 7^k-1 is divisible by 6, and 6 is divisible by 6, so 7(7^k-1)+6 is divisible by 6

    since 6a+6b = 6(a+b)

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