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Thread: 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 $\displaystyle p_{1}^m_{1}p_{2}^m_{2}\dots p_{q}^m_{q}$. Show that $\displaystyle \sqrt n$ can be written as a fraction if and only if $\displaystyle m_{i} (1 \leq i \leq q)$.


    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 $\displaystyle p_{1}^m_{1}p_{2}^m_{2}\dots p_{q}^m_{q}$. Show that $\displaystyle \sqrt n$ can be written as a fraction if and only if $\displaystyle m_{i} (1 \leq i \leq q)$. 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 $\displaystyle p_{1}^m_{1}p_{2}^m_{2}\dots p_{q}^m_{q}$. Show that $\displaystyle \sqrt n$ can be written as a fraction if and only if $\displaystyle m_{i} (1 \leq i \leq q)$ 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 $\displaystyle p_{1}^m_{1}p_{2}^m_{2}\dots p_{q}^m_{q}$. Show that $\displaystyle \sqrt n$ can be written as a fraction if and only if $\displaystyle m_{i} (1 \leq i \leq q)$.


    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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