Let Zₙ = {[0]ₙ),[1]ₙ,[n-1]ₙ} for any natural number n, where[r]_(n)represents the equivalent class of r modulo n.
Define f(ₙ,ₘ) : Zₙ →Zₘ by f (ₙ,ₘ) ([r])ₙ = [r]ₘ. Find sufficient condition on n and m that makes f(ₙ,ₘ) a function. Justify (prove) your answer.
