Universal chord theorem

In mathematical analysis, the universal chord theorem states that if a function f is continuous on [a,b] and satisfies ${\displaystyle f(a)=f(b)}$, then for every natural number ${\displaystyle n}$, there exists some ${\displaystyle x\in [a,b]}$ such that ${\displaystyle f(x)=f\left(x+{\frac {b-a}{n}}\right)}$.