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1

Part of 1993 Japan MO Finals

Problems(1)

Prove that w_1 or w_2 is not periodic.

Source: Japan Mathematical Olympiad Finals 1993 , Problem 1

6/12/2006
Call a word forming by alphabetical small letters a,b,c, ⋯x,y,za,b,c,\ \cdots x,y,z and a periodic word arranging by a certain word more than two times repeatedly.For example kyonkyon is eight-letter periodic word. Given two words W1, W2W_1,\ W_2 which have the same number of letters and have a different first letter, if you will remove the letter, W1W_1 and W2W_2 will be same word.Prove that either W1W_1 or W2W_2 is not periodic.
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