Lambda Calculus – Defining lambda term to represent function $f(n) = true$ if $n$ even and $false$ otherwise

Question

I have a problem with Exercise 7 from Selinger's notes on Lambda Calculus. Here there is the exercise:

Find a lambda term that represent the function: $$f (n) := \begin{cases} \mathbf{T}, \text{ if } n \text{ even,}\\ \mathbf{F}, \text{ otherwise}.\\ \end{cases} $$ with $\mathbf{T} \equiv \lambda a b.a$ and $\mathbf{F} \equiv \lambda a b.b.$

Quite simply, I just don't see how we can obtain something like this without having a definition of division. How should the solution look like?

Any feedback would be greatly appreciated.
Thank you for your time.

Answer 1

Hint. $0$ is even, and everything else has the opposite parity of its predecessor.