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by kvcpk » Thu Aug 12, 2010 3:38 am
taim wrote:If the integer n has exactly 3 positive divisors, including 1 and n, how many positive integers does n^2 have?
Question is asking a general rule. Hence you can use substitution.

Take for example: n=4
4 has divisors:1,2,4 = 3 divisors
4^2 =16 has 1,2,4,8,16 = 5 divisors

Hence answer should be 5 including 1 and n.

Hope this helps!!
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by sanju09 » Thu Aug 12, 2010 3:38 am
taim wrote:If the integer n has exactly 3 positive divisors, including 1 and n, how many positive integers does n^2 have?
Only square of primes have exactly 3 divisors including 1 and the prime. Hence n can be put equal to x^2 where x is prime. Now n^2 = x^4, which will have [spoiler]5[/spoiler] positive divisors, including 1 and n.
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