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Unformatted text preview: In the contrary case, all of the S k have a nonzero remainder when divided by 1998. By the pigeonhole principle (there are 1998 sums but only 1997 possible remainder  1 to 1997) two of the sums must have the same remainder upon division by 1998. The difference of these two sums is divisible by 1998. this page....
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 Spring '10
 AlbertoDelgado
 Combinatorics, Division, Elementary arithmetic, Bradley University, Terauchi Kimio

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