Difference between revisions of "1999 IMO Problems/Problem 6"
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Determine all functions <math>f:\Bbb{R}\to \Bbb{R}</math> such that | Determine all functions <math>f:\Bbb{R}\to \Bbb{R}</math> such that | ||
| − | <cmath>f(x-f(y)) | + | <cmath>f(x-f(y))=f(f(y))+xf(y)+f(x)-1</cmath> |
for all real numbers <math>x,y</math>. | for all real numbers <math>x,y</math>. | ||
Revision as of 23:02, 18 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
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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 | ||
