Science:Math Exam Resources/Courses/MATH312/December 2005/Question 01
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Question 01 

True or False Suppose that n is an integer with exactly 3 possible divisors. Then for some prime p. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
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Hint 

Suppose a number has at least two distinct prime divisors. What is a lower bound on the number of divisors in this case? 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The answer is true. Suppose that n has at least two distinct positive divisors p and q. Then it has at least 4 prime divisors given by . Thus n must only have one prime divisor. Then if , then n has prime divisors. Thus if we have that which is as claimed in the question. 