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Math Help - about factorization of Prime numbers ... !

  1. #1
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    about factorization of Prime numbers ... !

    Hi there. I am trying to solve this problem and until now I am unable. Can someone help me in finding the solution of this problem.

    -------------------------
    Let n be a (unique) prime factorization of p_{1}^m_{1}p_{2}^m_{2}\dots p_{q}^m_{q}. Show that \sqrt n can be written as a fraction if and only if m_{i} (1 \leq i \leq q).


    This is very urgent request. Please help me
    Bundle of thanks in advance.
    Kashi
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  2. #2
    Senior Member abhishekkgp's Avatar
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    Re: about factorization of Prime numbers ... !

    Quote Originally Posted by kashnex View Post
    Hi there. I am trying to solve this problem and until now I am unable. Can someone help me in finding the solution of this problem.

    -------------------------
    Let n be a (unique) prime factorization of p_{1}^m_{1}p_{2}^m_{2}\dots p_{q}^m_{q}. Show that \sqrt n can be written as a fraction if and only if m_{i} (1 \leq i \leq q). what do you mean if and only if m_i. this statement is not complete.


    This is very urgent request. Please help me
    Bundle of thanks in advance.
    Kashi
    ...
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  3. #3
    Super Member TheChaz's Avatar
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    Re: about factorization of Prime numbers ... !

    Quote Originally Posted by kashnex View Post
    Hi there. I am trying to solve this problem and until now I am unable. Can someone help me in finding the solution of this problem.

    -------------------------
    Let n be a (unique) prime factorization of p_{1}^m_{1}p_{2}^m_{2}\dots p_{q}^m_{q}. Show that \sqrt n can be written as a fraction if and only if m_{i} (1 \leq i \leq q) are even.


    This is very urgent request. Please help me
    Bundle of thanks in advance.
    Kashi
    So far, a few hints have been discussed at http://www.mymathforum.com/viewtopic.php?f=40&t=22048
    FYI...
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  4. #4
    Grand Panjandrum
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    Re: about factorization of Prime numbers ... !

    Quote Originally Posted by kashnex View Post
    Hi there. I am trying to solve this problem and until now I am unable. Can someone help me in finding the solution of this problem.

    -------------------------
    Let n be a (unique) prime factorization of p_{1}^m_{1}p_{2}^m_{2}\dots p_{q}^m_{q}. Show that \sqrt n can be written as a fraction if and only if m_{i} (1 \leq i \leq q).


    This is very urgent request. Please help me
    Bundle of thanks in advance.
    Kashi
    The square root of an integer is rational if and only if the integer is a perfect square.

    CB
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