RU-ALLRUSSIAN 1983 Problem 2
Three positive integers are written on a blackboard. A move consists of replacing one of the numbers by the sum of the other two less one. For example, if the numbers are 3, 4, 5, then one move could lead to 4, 5, 8 or 3, 5, 7 or 3, 4, 6. After a series of moves the three numbers are 17, 1967 and 1983. Could the initial set have been 2, 2, 2? 3, 3, 3?
Dataset text NuminaMath olympiads. Quoted with source.
Solutions
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