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Let P (n) denote the number of factors of n. Find all values of  n which satisfy 

\(P(n)^2 =n\)

and justify your solution.

 Jul 30, 2020
 #1
avatar+111232 
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I am confused, what is squared?

 Jul 30, 2020
 #2
avatar+31212 
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I think it means like the following Melody:

 

Consider n = 9.  The factors of 9 are 1, 3 and 9. That is, there are three factors, so P(9) = 3, which means P(9)^2 = 9.

 

On the other hand the factors of 6 are 1, 2, 3 and 6 so P(6) = 4, hence P(6)^2 > 6

 

The question is asking for all the values of n that are like my first example (I think!).

Alan  Jul 30, 2020
 #3
avatar+111232 
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ok, so you think 

 

P(n)^2 =n    means

 

[ P(n) ]^2 =n

 

Yes, that is probably what is meant.

Melody  Jul 30, 2020

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