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?

LiIIiam0216 Jun 21, 2024

#1**+1 **

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! :)

NotThatSmart Jun 21, 2024