In addition to the good answer from hops, have a look at the following python code, which can illustrate this behavior:
Fs = 700.0
T = 1.
N = Fs*T
f0 = 5# change to something else, how you want
Nc = f0*T
t = np.arange(0, T, 1/Fs)
signal = np.sin(2*np.pi*f0*t)
print N, Nc
B = 2 # number of bits used for quantization
A = 1. # (one-sided) amplitude
delta = (2*A) / (2**B-1)
threshs = -A + delta * np.arange(2**B)
def quantize(signal, threshs):
# performs the quantization (for newer python version, you can have a look at numpy.digitize)
T = threshs.reshape((1, -1))
S = signal.reshape((-1,1))
diff = S - T
quantized = threshs[np.argmin(abs(diff), axis=1)]
quantized = quantize(signal, threshs)
qnoise = quantized - signal
plt.plot(t, quantized, 'r-')
plt.title('Fs=%.0f, f0=%.0f, N=%.1f Nc=%.1f' % (Fs, f0, N, Nc))
plt.plot(t, qnoise, 'g-')
f = np.linspace(-Fs/2, Fs/2, len(t), endpoint=False)
spec = lambda x: 20*np.log10(abs(np.fft.fftshift(np.fft.fft(x))))
plt.plot(f, spec(signal), label='signal')
plt.plot(f, spec(qnoise), label='noise')
Here are two outputs, for different Fs:
As visible, the peak for the 5Hz signal is very clear, for both sampling frequencies. But, the noises look different. When N and Nc are not coprime, the noise is quite discrete (i.e. it shows strong peaks), but still, it is distributed everywhere in frequency domain. Looking at the coprime example (5 and 573), we see a bit more distributed noise, but still it exhibits strong peaks in the frequency domain.
Looking at the time-domain realization of both noises, it can be seen that both exhibit a decent periodicity. This periodicity creates the peaks in the frequency domain, regardless of whether the signal contains a full period of the noise or not.
So, with the above results, I would actually question the mentioned slides, which state the noise is uniformly distributed in the frequency domain. It is not, as any periodic time-domain signal will create periodic quantization noise, and hence create a (roughly) discrete noise spectrum.
This is the result with 16 bit quantization (i.e. B=16):
As visible, the effect is very different from the coarse quantization with 2bits above: For coprime numbers, the noise looks uniformly distributed. For matching numbers, the noise becomes discrete in frequency domain. This confirms the OPs claim. So, it depends strongly on the number of bits used for quantization.
I have just increased the frequency of the signal to 250Hz. Now N=700 and Nc=250 (which are not coprime, both dividable by 50), the spectrum of the noise is still relatively uniform, but has some small peaks. So, the claim from the OP is really depending on the actual parameters. Only coprime-ness seems not to be sufficient. Anyway, it's an interesting thing to play around with.