I'm solving a problem to which the final obstacle (I think) is knowing if this function is even or odd:
Given $$xQ(x+2018)=(x-2018)Q(x)$$ and that $Q(1)=1$, what is $Q(2017)$?
My best attempt so far is plugging in $x =-1$ to which I got $$(-1)Q(-1+2018)=(-1-2018)Q(-1)$$ $$Q(2017)=(2019)Q(-1)$$ I can simply conclude $Q(2017)=2019$ if I can prove $Q(-1)=Q(1)$ which brings me to the question how can I prove that $xQ(x+2018)=(x-2018)Q(x)$ is an even function? I've only been used to identifying odd and even functions for the usual polynomial/rational functions with exponents and all.
I would really appreciate the help. Thank you!