The procedure for a quantum period-finding algorithm is described on page 236 of "Quantum Computation and Quantum Information" by Isaac Chuang and Michael Nielsen. In step 3 of the procedure, authors introduce state $|\hat f(l)> = \frac{1}{r} \sum_{x=0}^{r-1} \exp(-2 \pi i lx /r) |f(x)>$. In excercise 5.20 we are asked to relate that result to canonical form of Fourier transform of descrite function $ \hat f(l) = \frac{1}{N} \sum_{x=0}^{N-1} \exp (- 2 \pi l x /N)$. This is fairly easy since we are given a hint that $$ \sum_{k \in \{ 0,r,2r,\dots,N-r \}} \exp(2 \pi ikl/N) = \sqrt \frac{N}{r} $$ if $l$ is an integer multiple of $N/r$.
But this is clearly not true and that is even stated in errata* list for that book. There should be no square root in that last equation.
Does it mean that there is also a mistake in step 3 of that algorithm? I doubt that authors wouldn't include that in errata if that was a case, but there is something clearly missing in reasoning presented by the authors.
*http://www.michaelnielsen.org/qcqi/errata/errata/errata.html