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 M, N we have .
Thus, we also have also, so by the Chinese Remainder Theorem . Thus, ends in the digit 9, as desired.
|1998 USAMO (Problems • Resources)|
|1 • 2 • 3 • 4 • 5 • 6|
|All USAMO Problems and Solutions|