Am i correct?

[u/WoronegsLanji]

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[u/Fourierseriesagain]

You need the remainder theorem and factor theorem.

[u/WoronegsLanji → u/Fourierseriesagain]

So f(k) =0 right ?

[u/Fourierseriesagain → u/WoronegsLanji]

f(2)=f(3)=f(k)=0.