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Turkey TST Functional Equality

Source: Turkey Team Selection Test 2017 P7

April 6, 2017
algebraTSTfunctional equation

Problem Statement

Let aa be a real number. Find the number of functions f:R→Rf:\mathbb{R}\rightarrow \mathbb{R} depending on aa, such that f(xy+f(y))=f(x)y+af(xy+f(y))=f(x)y+a holds for every x,y∈Rx, y\in \mathbb{R}.
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