Difference between revisions of "2017 IMO Problems/Problem 2"
(Undo incomplete solution (only accounts for integers)) (Tag: Undo) |
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+ | ==Problem== | ||
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Let <math>\mathbb{R}</math> be the set of real numbers , determine all functions | Let <math>\mathbb{R}</math> be the set of real numbers , determine all functions | ||
− | <math>f:\mathbb{R}\rightarrow\mathbb{R}</math> such that for any real numbers <math>x</math> and <math>y</math> <math>{f(f(x)f(y)) + f(x+y)}< | + | <math>f:\mathbb{R}\rightarrow\mathbb{R}</math> such that for any real numbers <math>x</math> and <math>y</math> |
+ | |||
+ | <math></math>{f(f(x)f(y)) + f(x+y)}<math> =</math>f(xy)<math></math> | ||
+ | |||
+ | ==Solution== | ||
+ | {{solution}} | ||
+ | |||
+ | ==See Also== | ||
+ | |||
+ | {{IMO box|year=2017|num-b=1|num-a=3}} |
Revision as of 01:39, 19 November 2023
Problem
Let be the set of real numbers , determine all functions
such that for any real numbers
and
$$ (Error compiling LaTeX. Unknown error_msg){f(f(x)f(y)) + f(x+y)}f(xy)$$ (Error compiling LaTeX. Unknown error_msg)
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
2017 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |