SOLUTION: Suppose 2001 is divided by an integer n. For which integers n is the remainder 9?

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Question 420129: Suppose 2001 is divided by an integer n. For which integers n is the remainder 9?
Answer by robertb(5830) About Me  (Show Source):
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We have 2001%2Fn+=+q++%2B+9%2Fn, or 1992%2Fn+=+q, where q is a positive integral quotient. Now 1992 = 2%5E3%2A3%2A83. We want n to be relatively prime to 9, AND greater than 9. From the prime factorization of 1992, the only possible values of n are 83 (a prime number), 2*83 = 166, 2%5E2%2A83+=+332, 2%5E3%2A83+=+664.