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(2011 Philippine Math Olympiad ) Find all
such that -
Solution: Consider
, Next, consider
to get Next consider
Combining with the above, we get
Finally to get -
Solution: Now either
or . If
then and and which is a contradiction If
then and which is a contradiction -
Answer: No such function exists
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See here Find function(s)
such that -
Solution Let
Then .
Then. Using
. Using it again gives
Combine this with the original equation
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Solution: Another solution is to consider
and . If , then So that
. Choose any such that and .
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