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Math Help - Discrete Math Proofs -- Need Help

  1. #1
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    Discrete Math Proofs -- Need Help

    Some practice problems that I am stuck on, in my first week of this class.

    Prove that 1^3+2^3...+n^3 = (1+2+...n)^2

    Prove that 11^n+1 + 12^n+1 is divisible by 133

    I can only show that these are true by using examples (i.e plugging stuff in). I don't know how to do the proof for either one.
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    Hello,
    Quote Originally Posted by goldenratio999 View Post
    Some practice problems that I am stuck on, in my first week of this class.

    Prove that 1^3+2^3...+n^3 = (1+2+...n)^2

    Prove that 11^n+1 + 12^n+1 is divisible by 133

    I can only show that these are true by using examples (i.e plugging stuff in). I don't know how to do the proof for either one.
    Both problems can be solved by induction
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    so for the first one I would prove that the statement is true for 1 to 2 (minimum set/basis case) then prove that it if its true for some n (that i don't need to specify), that it must be true for n+1?

    for the second one i would probe that its true for n=1, and then what? prove that if its true for some n, that it must be true for n+1 again? or something else?

    I will do these quickly and show you if that's ok, I want to make sure I understand this correctly.

    thanks

    EDITED
    Last edited by goldenratio999; January 28th 2009 at 02:28 AM. Reason: made mistake sorry
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