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Math Help - Induction

  1. #1
    Senior Member DivideBy0's Avatar
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    Induction

    Use the method of mathematical induction to prove that 4^n+14 is a multiple of 6 for n \geq 1.

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  2. #2
    Eater of Worlds
    galactus's Avatar
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    Let's see if this holds water.

    4^{1}+14=18, true.

    Assume 6 is a factor of 4^{k}+14. The (k+1)st term is

    4^{k+1}+14=4\cdot{4^{k}}+14

    = 4\cdot{4^{k}}+56-42=4(4^{k}+14)-42

    By the induction hypothesis, 6 is a factor of 4^{k}+14 and

    6 is a factor of 42, so 6 is a factor of the (k+1)st term and P_{k+1}<br /> <br />
is true. And QED.
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