1998 USAMO Problems/Problem 1
Suppose that the set has been partitioned into disjoint pairs () so that for all , equals or . Prove that the sum ends in the digit .
Notice that , so .
Also, for integers we have .
Thus, we also have also, so by the Chinese Remainder Theorem . Thus, ends in the digit 9, as desired.
FASTEST SOLVE ON STREAM from v_Enhance (:omighty:) https://www.youtube.com/watch?v=jsw3c3yAn7o
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