Let a>0 and f:R→R a function such that f(x)+f(x+2a)+f(x+3a)+f(x+5a)=1 for all x∈R . Show that f is periodic, that is, that there is some b>0 for which f(x)=f(x+b) for every x∈R holds. Find the smallest such b, which works for all these functions . periodicfunctionalfunctional equationalgebra