let $f:[0,1]\longrightarrow [0,1]$ be a continuous function such that $f(0)=f(1)$, show that : if the number $l$ is not of the form $\dfrac{1}{n}$ there exsits a function of this form on whose graph one cannot inscrible a horizontal chord of length $l$
This problem is from $Mathematical Analysis (Zorich) P170,problem 7(2),Thank you evryone