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Math Help - Help on Mobius function

  1. #1
    Junior Member
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    Help on Mobius function

    Show that if n is a positive integer, then
    \mu(n)\mu(n+1)\mu(n+2)\mu(n+3) = 0

    I know that's mean one of the \mu above has a square factor.
    Sure at least one \mu(n),\mu(n+1),\mu(n+2),\mu(n+3) of it is even and it must be power of 2 but how can I write it down properly as a proof?

    Help you for your help.
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  2. #2
    Super Member PaulRS's Avatar
    Joined
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    Among 4 consecutive natural numbers one must be divisble by 4

    You can separate in cases n\equiv{0;1;2;3}(\bmod.4)
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