Question: Write the numbers 1, 2, . . . , 2k on a paper, where k is an odd integer. choose any two of the numbers,

Write the numbers 1, 2, . . . , 2k on a paper, where k is an odd integer. choose any two of the numbers, x and y, write |x y| down and then erase x and y. Continue doing this until only one integer is written down. Prove that this integer must be odd.

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