Problem 1008

[jj_rabeyrin]

I'm probably doing a stupid mistake but i don't understand the example (2,7).
Why Q(x) = x^2 would not be ok /better ?
then Q(n^2 ) = n^4
and n^4 = n mod 7 for n=0,1,2.

Any advice of what i'm missing please?

[Icy]

You're not missing anything. It's a genuine error/typo with the problem statement. As evidenced by the example, the authors wanted the functional inverse to be monic with prescribed degree $N+1$, i.e. the coefficient of $x^{N+1}$ has to be 1.