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IMO Shortlist 2012, Algebra 5

Source: IMO Shortlist 2012, Algebra 5

July 29, 2013
functionalgebrafunctional equationIMO Shortlist

Problem Statement

Find all functions f:R→Rf:\mathbb{R} \rightarrow \mathbb{R} that satisfy the conditions f(1+xy)-f(x+y)=f(x)f(y)   \text{for all } x,y \in \mathbb{R}, and f(−1)≠0f(-1) \neq 0.
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