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Question

All numbers from 1 to 1966 are written on a blackboard.

You are allowed to erase any two numbers and write their difference instead.

Prove that repetition of that operation may not result in having only zeroes on the blackboard.


(Problem from Russian Math Olympiads. 6-th grade, 1966.)

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The operation decreases the sum of all numbers by even number, but (1+2+...+1966) is odd.

Nice. When at math competition, solve it like this and you have extra time to tackle other problems.

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