# 2016 is absolutely awesome 18

Algebra Level 4

How many functions $$f:\mathbb{N}\rightarrow\mathbb{N}$$ such that:

• $$f(20160) = 1$$

• for all $$x$$ and $$y$$, $$f(xy) = f(x)f(y)$$

• for any $$n$$ whose last digit is 3, $$f(n) = 1$$.

Classification:

• $$\mathbb{N}=\{0; 1; 2; 3; \ldots\}$$

×