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III Lusophon Mathematical Olympiad 2013 - Problem 3

Source:

August 12, 2013

Problem Statement

An event occurs many years ago. It occurs periodically in xx consecutive years, then there is a break of yy consecutive years. We know that the event occured in 19641964, 19861986, 19961996, 20082008 and it didn't occur in 19761976, 19931993, 20062006, 20132013. What is the first year in that the event will occur again?
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