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Thread: Exponent question help please

  1. #1
    Junior Member
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    Exponent question help please

    For what integral values of n is the expression (*-means to the)))

    ( 1*n+ 2*n +3*n +4*n ) divisible by 5

    thanks so much for the help

    i think it must be a multiple by three but i dont know how to prove it
    Last edited by anime_mania; Feb 10th 2008 at 07:28 PM. Reason: more to add
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  2. #2
    Senior Member topher0805's Avatar
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    I'm not sure I understand your post.

    Is this what you mean?

    For what value of $\displaystyle n$ is this expression divisible by $\displaystyle 5$?

    $\displaystyle 1^n + 2^n + 3^n + 4^n$

    Note that $\displaystyle 1 + 2 + 3 + 4 = 10$, which is divisible by $\displaystyle 5$.

    So, for what value of n are $\displaystyle 1^n$, $\displaystyle 2^n$, $\displaystyle 3^n$, and $\displaystyle 4^n$ equal to $\displaystyle 1$, $\displaystyle 2$, $\displaystyle 3$ and $\displaystyle 4$, respectively?

    The answer to this is of course $\displaystyle 1$. If you take anything to the power of $\displaystyle 1$, it will be equal to itself.

    If you need to find all values of $\displaystyle n$ for which this expression is divisible by $\displaystyle 5$, note that every odd integer $\displaystyle n$ gives a number that is divisible by $\displaystyle 5$.
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