Difference between revisions of "1999 IMO Problems/Problem 6"
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| − | + | ==Problem== | |
| − | + | ||
| + | Determine all functions <math>f:\Bbb{R}\to \Bbb{R}</math> such that | ||
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| + | <cmath>f(x-f(y))=f(f(y))+xf(y)+f(x)-1</cmath> | ||
| + | |||
| + | for all real numbers <math>x,y</math>. | ||
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| + | ==Solution== | ||
| + | {{solution}} | ||
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| + | ==See Also== | ||
| + | |||
| + | {{IMO box|year=1999|num-b=5|after=Last Question}} | ||
[[Category:Olympiad Algebra Problems]] | [[Category:Olympiad Algebra Problems]] | ||
[[Category:Functional Equation Problems]] | [[Category:Functional Equation Problems]] | ||
Latest revision as of 00:02, 19 November 2023
Problem
Determine all functions 
such that
![\[f(x-f(y))=f(f(y))+xf(y)+f(x)-1\]](http://latex.artofproblemsolving.com/e/e/c/eec1fb7e4c810e8f31de524acf1b4bb5f71ffeb8.png)
for all real numbers 
.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 1999 IMO (Problems) • Resources | ||
| Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Last Question |
| All IMO Problems and Solutions | ||
