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Math Help - Have no idea on how to prove

  1. #1
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    Have no idea on how to prove

    Can someone help me prove that 2^3^n + 1 is divisible by 3^(n+1)??!!
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  2. #2
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    Re: Have no idea on how to prove

    you've not performed induction before?

    for n = 1 , 2^{3^n} + 1 = 9 , 3^{n+1} = 9 ... true for n = 1

    assume true for n , prove true for n+1 ...

    2^{3^{n+1}} + 1 = 2^{3^n \cdot 3} + 1 = (2^{3n})^3 + 1

    the last expression is the sum of two cubes and will factor. can you finish?
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