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

For prime number we have :



where d is a divisor function .

Quote:

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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

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Think of it this way. If is a divisor of then so is The integer is a perfect square if and only if it has a divisor such that