Write the numbers 1 , 2, ... , 2n on a blackboard, where n

Chapter 1, Problem 1.7.23

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Write the numbers 1 , 2, ... , 2n on a blackboard, where n is an odd integer. Pick any two of the numbers, j and k, write Ij - kl on the board and erase j and k. Continue this process until only one integer is written on the board. Prove that this integer must be odd.

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