Difference between revisions of "2008 iTest Problems/Problem 80"
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Revision as of 17:49, 16 September 2008
Problem
Let
and let be the polynomial remainder when is divided by . Find the remainder when is divided by .
Solution
. We apply the polynomial generalization of the Chinese Remainder Theorem.
Indeed,
since . Also,
using similar reasoning. Hence , and by CRT we have .
Then .