document.write( "Question 266539: How many positive integers n produce a remainder of 9 when 2009 is divided by n and n > 9 ? \n" ); document.write( "

Algebra.Com's Answer #195823 by drk(1908) $\"\"$ $\"About$

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Well we can't use the numbers 1 - 9. All remainders will be less than 9.
\n" ); document.write( "take 2009 - 9 and we get 2000. We are looking for all factors of 2000 greater than 9.
\n" ); document.write( "using prime factorization , we get 2^4 x 5^3. Using Euler's idea, there are 5x4 = 20 factors, but we don't want: 1, 2, 4, 5, or 8, so we end with 15 answers.
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\n" ); document.write( "n = 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000 \n" ); document.write( "

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