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Math Help - why is a perfect square has odd number of distinct factors?

  1. #1
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    why is a perfect square has odd number of distinct factors?

    Can some one show me how to proof this? or this is just common sense?

    Eg: 36:2,3,6
    4: 2
    9: 3

    Thanks
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  2. #2
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    Re: why is a perfect square has odd number of distinct factors?

    For prime number p we have :

    d\left(p^n\right)=n+1

    where d is a divisor function .
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  3. #3
    Member Sylvia104's Avatar
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    Re: Why does a perfect square have odd number of distinct factors?

    Quote Originally Posted by cmath View Post
    Can some one show me how to proof this? or this is just common sense?

    Eg: 36:2,3,6
    4: 2
    9: 3

    Thanks
    Think of it this way. If d is a divisor of n, then so is \frac nd. The integer n is a perfect square if and only if it has a divisor d such that d=\frac nd.
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