Idempotents à la mod
An idempotent satisfies the equation x2 = x. In ordinary arithmetic, this is so easy to solve it’s boring. We delight the mathematical palette here, topping idempotents off with modular arithmetic and a series of exercises determining for which n there are more than two idempotents (mod n) and exactly how many there are.
Sibley TQ. 2012. Idempotents à la mod. The College Mathematics Journal 43(5): 401-404.