Difference between revisions of "2009 IMO Problems/Problem 1"
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== Solution == | == Solution == |
Revision as of 06:23, 23 July 2009
Problem
Let be a positive integer and let
be distinct integers in the set
such that
divides
for
. Prove that
doesn't divide
.
Author: Ross Atkins, Australia
--Bugi 10:23, 23 July 2009 (UTC)Bugi
Solution
Let such that
and
. Suppose
divides
.
Note
implies
and hence
. Similarly one has
for all
's, in particular,
and
force
. Now
gives
, similarly one has
for all
's, that is
's satisfy
and
, but there should be at most one such integer satisfies them within the range of
for
and
. A contradiction!!!
Solution by ychjae