Question

If the integer n has exactly three positive divisors, including 1 and n how many positive divisors does n^2 have?

Answer 1

suppose the three divisors of n are 1 , x and n then,
the divisors of n^2 are 1 , x ,x^2 , nx , n and n^2

Answer 2

so, there will be 6 positive divisors of n^2

Answer 3

got it?

Answer 4

ya i took some egs .. n is der ne formule for tis cz i've the soln wer they hav given weird formula!!!

Answer 5

Let us take an Example:

Suppose n = 4:

So:

Divisors are : 1, 2 and 4..

Now : \(4^2 =16\)

Divisors are : 1, 2, 4, 8, 16 (5 Divisors)..

Answer 6

Oh sorry the answer is five... actually x^2 and n will be same because n has only three factors which are 1 , x and n
So, n = 1*n or x*x

Answer 7

Now this is right @sauravshakya ..