6

Part of 2012 Kyrgyzstan National Olympiad

Problems(1)

1 through 50 on blackboard; replace any two with difference

Source: Kyrgyzstan 2012, Problem 6

1, 2,\ldots, 50

are written on a blackboard. Each minute any two numbers are erased and their positive difference is written instead. At the end one number remains. Which values can take this number?

invariantmodular arithmeticinductionalgorithmcombinatorics unsolvedcombinatorics