# Thread: about factorization of Prime numbers ... !

1. ## 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.

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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

2. ## Re: about factorization of Prime numbers ... !

Originally Posted by kashnex
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
...

3. ## Re: about factorization of Prime numbers ... !

Originally Posted by kashnex
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...

4. ## Re: about factorization of Prime numbers ... !

Originally Posted by kashnex
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