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A positive integer is called terrific if it has exactly $3$ positive divisors.   What is the smallest number of primes that could divide a terrific positive integer?

 Jun 21, 2024
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In order for a number to be terrific, then it must be divisble by 1, itself, and be a perfect square. 

Let's say x is a terrific number. 

 

It has to be divisble by x and 1, and be a perfect square. 

\(25\) is a perfect example. 

 

However, let's note that it has to be a perfect square for a prime number, because if the squared number was composite, there would be another divisor. 

 

Thus, the minimum number of primes is \(1\)

 

So 1 is our answer. 

 

Thanks! :)

 Jun 21, 2024

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