Question 01 (b)
Short answer questions: Each question carries 6 marks, your answers should quote the results being used and show your work.
For which positive integers m will
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!
Isolating, we seek to find integers m such that
What must m divide?
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.
As stated in the hint, the given problem is equivalent to
Thus m must be a divisor of 999. We can factor 999 as
Thus, the divisors are and these are the potential m values.