I am teaching a Linear Algebra class for first year students and one problem we are discussing in class is the fact that the sum of all elements in a finite field $F$ is $0$ if $|F|>2$. This result is not true in $\mathbb F_2$, a colloquial explanation would be that there is not enough "space" in $\mathbb F_2$.
What are some other nice and interesting examples of theorems that are true except for "small" values or boundary cases? (basic or advanced, from any area of maths, ...)
