Consider functions f from the whole numbers (non-negative integers) to the whole numbers that have the following properties:
∙ For all x and y, f(xy)=f(x)f(y),
∙ f(30)=1, and
∙ for any n whose last digit is 7, f(n)=1.
Obviously, the function whose value at n is 1 for all n is one such function. Are there any others? If not, why not, and if so, what are they? functionfunctionalalgebrafunctional equation