KöMaL 2011 B4341

Find all pairs $f$ ( $x$ ), $g$ ( $x$ ) of polynomials of real coefficients such that $f$ ( $x$ +1) $g$ ( $x$ -1)- $g$ ( $x$ +1) $f$ ( $x$ -1)=1.

Official text KöMaL. Quoted with source.

Solutions

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