If the square root of p^2 is an integer greater than 1, which of the following must be true?
I. p^2 has an odd number of positive factors
II. p^2 can be expressed as the product of an even number of positive prime factors
III. p has an even number of positive factors
Choices:
A) I B) II C) III D) I and II E) II and III
It is given that p2−−√p2&gt;1 and is an integer..   Also p2−−√p2=p   so p^2 is a perfect square and p is an integer&gt;1..   lets see three statements:-   I. p^2 has an odd number of positive factors-- TRUE   A perfect square has an Odd number of perfect square ..   WHY? Because all factors will have a different integer as a pair except p..   p*p=p^2.. so that will be just one factor   II. p^2 can be expressed as the product of an even number of positive prime factors   again TRUE   25 =5*5 ; 49= 7*7 ; 36 = 2*2*3*3   III. p has an even number of positive factors..   Since it uses 'HAS', if we find one which does not follow the statement is not true..   we already know that A perfect square has an Odd number of perfect square ..   so if p is a perfect square itself ans is No   ONLY I and II are true   ANSWER:I and II
<result>D</result>
If the square root of p^2 is an integer greater than 1, which of the following must be true?
I. p^2 has an odd number of positive factors
II. p^2 can be expressed as the product of an even number of positive prime factors
III. p has an even number of positive factors