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Math Help - Prove by induction #2

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    Prove by induction #2

    Prove by induction:
    6*7^(n power) - 2*3^(n power) is divisible by 4, for all n is great than or equal to 1
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  2. #2
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    Quote Originally Posted by sderosa518 View Post
    Prove by induction:
    6*7^(n power) - 2*3^(n power) is divisible by 4, for all n is great than or equal to 1

    6*7^n - 2*3^n = 2*[3*7^n - 3^n] , and since the expression in the parentheses is odd this number is 2*2* something else, and we're done
    without any induction at all.

    Of course, you can try induction as well...

    Tonio
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    Quote Originally Posted by tonio View Post
    6*7^n - 2*3^n = 2*[3*7^n - 3^n] , and since the expression in the parentheses is odd this number is 2*2* something else, and we're done
    without any induction at all.

    Of course, you can try induction as well...

    Tonio
    I assume you meant that the expression in the parentheses is even! since 3*7^n and 3^n are odd numbers, and subtracting two odd numbers gives an even number.

    To solve by induction, simply follow the steps provided in the other topics you posted..
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