Let $f$ be a function such that $\int_{-\infty}^{+\infty}|f(x)|^{2} d x<\infty$. Prove that

$$\int_{-\infty}^{+\infty} f(x+k) \overline{f(x+l)} d x=0 \quad \text { for all integers } k \text { and } l \text { with } k \neq l,$$

if and only if

$$\int_{-\infty}^{+\infty}|\widehat{f}(t)|^{2} e^{-i m t} d t=0 \quad \text { for all integers } m \neq 0$$

where $\widehat{f}$ is the Fourier transform of $f$.