OG 11 math problem solving question

nuku888

Hello everyone,

I was wondering if anyone can help me with the explanation for question 241 in the OG11.

Question

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

I read the explanation at the back but I don't understand if anyone can explain that would be great thanks!

zaffar · Posted: Thu Apr 19, 2007 10:09 pm Post subject:

i did it by picking numbers and there are only 2 numbers 4 (three divisors 1 2 4) & 9 (1 3 9). and their squares 16 (1,2,4,8,16) and 81 (1,3,9,27,81)
so 5 is the answer.

there may be someother method but i did it this way. i hope it helps.

nuku888 · Posted: Fri Apr 20, 2007 3:09 pm Post subject:

Thanks for your reply. Sorry just got one more questions they mention something about square root n is also an integer, so does that mean square root 4 = 2 that is why they said that it is also integer?

sosaha · Posted: Sat Apr 21, 2007 11:33 pm Post subject:

lets consider the number to be 'n'. since it has only one more divisor other than 1 and n, n must be a perfect sqare. so say n=x^2(x is a prime).
=> n^2 = x^4
Now divisors of x^4 are 1, x, x^2, x^3, x^4.
i.e 5 divisors.