Science:Math Exam Resources/Courses/MATH312/December 2012/Question 02 (c)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q3 • Q4 • Q5 •
Question 02 (c) 

State whether the following are true or false with full justification. Each question carries 4 marks. The number 25 passes Miller's test for the base 7. 
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? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Recall that 7 passes Miller's test if
or the following holds for some r
where for and , and . If 7 passes the test, then 25 is a probable prime. If it fails the test, then the number is not prime. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. The answer is true. Recall that 7 passes Miller's test if
or the following holds for some r
where and . If 7 passes the test, then 25 is a probable prime. If it fails the test, then the number is not prime. So we check manually:
Thus, 7 passes Miller's test. (Note that 25 is not prime but still 7 passes Miller's test). 