+1. Ideally, you want 6, and in a 20 gallon tank. 3 is an incomplete school, incomplete schools = stress, and stress = lowered immune systems, and, sometimes, heightened aggression. Non-stressed tetras will not school tightly, but will spread out and swim alone, although still keeping other members of the group in sight.
Tetras aren't the easiest species to breed. They are susceptible to the usual diseases, the most common being ich.