SOLUTION: Suppose 2011 is divided by an integer n. For which integers n is the remainder 9?

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Question 420376: Suppose 2011 is divided by an integer n. For which integers n is the remainder 9?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We have 2011 ≡ 9 (mod n), so if we subtract 9 from both sides, we obtain 2002 ≡ 0 (mod n). Hence, we need to find all factors of 2002 greater than 9 (otherwise 2011 would not be 9 modulo n).

2002+=+%282%5E1%29%287%5E1%29%2811%5E1%29%2813%5E1%29. If you know the algorithm to finding the number of factors of a number, we conclude that the number has 16 factors. Only three of them (1,2,7) are less than 9, so the other 13 factors satisfy for n. I'll leave it to you to find the 13 factors of 2002 greater than 9.