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The number $100$ has four perfect square divisors, namely $1,$ $4,$ $25,$ and $100.$
What is the smallest positive integer that has exactly $2$ perfect square divisors?

 Nov 19, 2024
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The number $100$ has four perfect square divisors, namely $1,$ $4,$ $25,$ and $100.$    
What is the smallest positive integer that has exactly $2$ perfect square divisors?    

 

That would be 4.  Its two perfect square divisors are 1 and 4. 

 

We ignore 2 as a divisor of 4 because it isn't a perfect square,    

just as the example given in the problem ignored 10 and 20, etc.    

.    

 Nov 19, 2024

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