document.write( "Question 420129: Suppose 2001 is divided by an integer n. For which integers n is the remainder 9? \n" ); document.write( "

Algebra.Com's Answer #293639 by robertb(5830) $\"\"$ $\"About$

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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, $\"2%5E2%2A83+=+332\"$ , $\"2%5E3%2A83+=+664\"$ . \n" ); document.write( "

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