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pow:problem2s23

Problem 2 (due Monday, February 20)

Find all positive integers $n$ which have the following property: there is a continuous function $f:\mathbb R\longrightarrow \mathbb R$ such that for every real number $t$ the equation $f(x)=t$ has either no solutions or exactly $n$ different solutions.

We have not received any solutions. The positive integers in question are exactly all odd natural numbers. For a detailed solution see the following link Solution.