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Math Help - Discrete Math Help

  1. #1
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    Discrete Math Help

    I am new to Discrete Math. I am able to figure out how to do 1, 2, and 4 of the attachment, but do not have a clue where to start on the rest of the problems. Any help at all would be great. Thanks in advance.
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  2. #2
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    Hello, Hornedog20!

    3. What is the largest divisor of n^7 - n^3 for all  n \in N ?
    Are you sure of the wording?
    The largest divisor of {\color{blue}n^7-n^3} is, of course:
    . {\color{blue}n^7-n^3}
    Factor: . n^7-n^3 \;=\;n^3(n^4-1) \;=\;n^3(n^2-1)(n^2+1) \;=\;n^3(n-1)(n+1)(n^2+1)

    Then n^2+1 is the largest prime factor.

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  3. #3
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    Thanks for the reply. That is what I was thinking for #3 as well. I believe I have figured out 5, 6, and 7 now as well. I still am having problems with 8 and 9 though.
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