This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2016 USAJMO, 6
Tags: USAJMO , USA(J)MO , 2016 USAJMO , 2016 USAJMO Problem 6 , function , algebra , Hi
Find all functions $f:\mathbb{R}\rightarrow \mathbb{R}$ such that for all real numbers $x$ and $y$, $$(f(x)+xy)\cdot f(x-3y)+(f(y)+xy)\cdot f(3x-y)=(f(x+y))^2.$$

2016 USAMO, 4
Tags: USAJMO , USA(J)MO , 2016 USAJMO , 2016 USAJMO Problem 6 , function , algebra , Hi
Find all functions $f:\mathbb{R}\rightarrow \mathbb{R}$ such that for all real numbers $x$ and $y$, $$(f(x)+xy)\cdot f(x-3y)+(f(y)+xy)\cdot f(3x-y)=(f(x+y))^2.$$