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find all polynomials

Source: bmo 1988

April 23, 2007
algebrapolynomialalgebra proposed

Problem Statement

Find all polynomials of two variables P(x,y)P(x,y) which satisfy P(a,b)P(c,d)=P(ac+bd,ad+bc),∀a,b,c,d∈R.P(a,b) P(c,d) = P (ac+bd, ad+bc), \forall a,b,c,d \in \mathbb{R}.
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