Difference between revisions of "2017 IMO Problems/Problem 2"
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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> |
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| + | <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 | ||
