Number 3 is the only correct sentence.

All three sentences are grammatically correct, but they have slightly different meanings. Here are some dialogue examples to illustrate: A: "I don't owe you anything." B: "And I don't owe you anything either." A: "That's fair. We two owe nothing to each." A: "I don't owe you anything." B: "Well, I don't owe you anything either." A: "I guess that's true. We two owe nothing to either." A: "I don't owe you anything." B: "And I don't owe you anything either." A: "So we're even. We two owe nothing to each other."

Number 3