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Ax + B[x] = Ay + B[y] no solutions except x = y, when A, B reals

Source: Brazilian Mathematical Olympiad 1985 P5

July 27, 2018
algebraequation

Problem Statement

A,BA, B are reals. Find a necessary and sufficient condition for Ax+B[x]=Ay+B[y]Ax + B[x] = Ay + B[y] to have no solutions except x=yx = y.