2014 USAMO Problems: Difference between revisions
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[[2014 USAMO Problems/Problem 1|Solution]] | [[2014 USAMO Problems/Problem 1|Solution]] | ||
===Problem 2=== | ===Problem 2=== | ||
Let <math>\mathbb{Z}</math> be the set of integers. Find all functions <math>f : \mathbb{Z} \rightarrow \mathbb{Z}</math> such that <cmath>xf(2f(y)-x)+y^2f(2x-f(y))=\frac{f(x)^2}{x}+f(yf(y))</cmath> for all <math>x, y \in \mathbb{Z}</math> with <math>x \neq 0</math>. | |||
[[2014 USAMO Problems/Problem 2|Solution]] | [[2014 USAMO Problems/Problem 2|Solution]] | ||
===Problem 3=== | ===Problem 3=== | ||
[[2014 USAMO Problems/Problem 3|Solution]] | [[2014 USAMO Problems/Problem 3|Solution]] | ||
be the set of integers. Find all functions 
such that ![\[xf(2f(y)-x)+y^2f(2x-f(y))=\frac{f(x)^2}{x}+f(yf(y))\]](http://latex.artofproblemsolving.com/9/f/d/9fdb11dbf102dfe0783b1d31466e276420e3913d.png)
for all 
with 
.
