Difference between revisions of "1998 USAMO Problems/Problem 1"
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[[Category:Olympiad Number Theory Problems]] | [[Category:Olympiad Number Theory Problems]] |
Revision as of 08:03, 13 September 2012
Problem
Suppose that the set has been partitioned into disjoint pairs
(
) so that for all
,
equals
or
. Prove that the sum
ends in the digit
.
Solution
If , then
.
For integers M, N we have .
So we also have also, so
.
See Also
1998 USAMO (Problems • Resources) | ||
Preceded by First Question |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAMO Problems and Solutions |