What's the deal with witches and broomsticks?

Like all good parents, I mindlessly pass on cultural traditions to my kids and usually don't have a clue where they came from. We decorate a tree in December, hide colored eggs on Easter, and in October we dress up and carve pumpkins, and my kids tape up pictures of witches on broomsticks on the window. I've heard theories about some of these other things, but where did the "witches flying on broomsticks" thing come from?

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