2011 IMO Problems/Problem 3
Let be a real-valued function defined on the set of real numbers that satisfies
for all real numbers
and
. Prove that
for all
.
Solution
Let be the given assertion.
Comparing
and
yields,
Suppose
then
Now
implies that
Then yields a contradiction.
From we get
thus we get
as desired.
~ZETA_in_olympiad