A5

Part of 2012 IMO Shortlist

Problems(1)

IMO Shortlist 2012, Algebra 5

Source: IMO Shortlist 2012, Algebra 5

Find all functions

f:\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) \neq 0

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