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Let $D$ be the largest divisor of $1001001001$ that does not exceed $10000$. Find the remainder when $D$ is divided by $7$.

Let $S = \{2006, 2007, 2008, \ldots, 4012 \}$. Let $K$ denotes the sum of the greatest odd divisor of each of the element of $S$. Find the value of $K$.

I don't understand how to solve this question. I have been trying hard to solve them.

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    i am sorry if the tags does not match the query2011-10-20
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    1001001001 = 7.11.13.101.9901 and it turns out 9901 is the largest factor which does not exceed 10000.2011-10-20
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    @ t.b this was the question in today's test. And they never taught us chinese2011-10-20
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    steve, some characters do not seem to be rendering correctly. Can you maybe take a screenshot of what the question looks like when you're seeing it?2011-10-20
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    @J.M.: That was UTF-8 encoding. I've replaced it by the encoded characters. Here's an [online UTF-8 decoder](http://software.hixie.ch/utilities/cgi/unicode-decoder/utf8-decoder).2011-10-20
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    Thanks @joriki! (*adds decoder to bookmarks*)2011-10-20
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    You've had three answers, and almost a week to think about them, and ... silence. Do you like any of the answers enough to vote them up, maybe even accept one? Do you dislike the answers enough to indicate why and what more we could do to make them acceptable? Are you still there?2011-10-24

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