Q: How many mathematicians does it take to change a lightbulb?
A: One. He gives it to six irishmen, thereby reducing the problem to an earlier joke.
A: If k mathematicians can change a lightbulb, and if one more simply watches them do it, then k + 1 mathematicians will have changed the lightbulb. As was just shown, one mathematician can change a lightbulb. Therefore, by induction, it takes n mathematicians to change a lightbulb for any positive integer n.