Suppose that f is a continuous function on the interval [0,1] and that f(0) = f(1).

If n is an integer greater than 2, show that:

f(a) = f(a + (1/n) ) for some $\displaystyle a \in [0,1 - (1/n)] $.

How would I approach this question? Would I need to apply mathematics induction?

Thanks, any help will be highly appreciated.