Question
The following numbers are written on the board: `1, 2, 3, …, 2016, 2017`. In one move, it is allowed to choose a pair of numbers written on the board, erase them, and write their (positive) difference in their place. After several such operations, a single number remains on the board. Is it possible that this is zero?
Difficulty level (1 very easy - 10 very hard): 3
Topics:
Arithmetic
Combinatorics
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Invariants
Combinatorics
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Induction (Mathematical Induction)
Number Theory
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Division
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Parity (Even/Odd)
Algebra
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Sequences
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Arithmetic Progression / Arithmetic Sequence
Combinatorics
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Case Analysis / Checking Cases
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Processes / Procedures
Proof and Example
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Proof by Contradiction
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