Was going through the divisibility chapter and stumbled across this excercise that kinda stumped me.

Let be and integer. prove that . (Hint: Consider three cases.)

Now I see the answer as being evident. 3 divides or is a multiple of 1 of 3 consecutive numbers. lists 3 consecutive number so 3 is definitely going to divide their product. I'm just lost on how exactly to write the proof ... I hate divisibility chapter. The entire section is riddled with things we take for granted but have a hard time proving Thanks for any help guys!

(Small note: This section is prior to congruence or modulo so I'd like to avoid using those to prove it.)