Re: Why does a perfect square have odd number of distinct factors?
Originally Posted by cmath
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 $\displaystyle d$ is a divisor of $\displaystyle n,$ then so is $\displaystyle \frac nd.$ The integer $\displaystyle n$ is a perfect square if and only if it has a divisor $\displaystyle d$ such that $\displaystyle d=\frac nd.$