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Part of 2011 Canadian Mathematical Olympiad Qualification Repechage

Problems(1)

Determine all pairs (m,n) - [Canadian Repêchage 2011]

Source:

1/15/2011
Determine all pairs (n,m)(n,m) of positive integers for which there exists an infinite sequence {xk}\{x_k\} of 00's and 11's with the properties that if xi=0x_i=0 then xi+m=1x_{i+m}=1 and if xi=1x_i = 1 then xi+n=0.x_{i+n} = 0.
inductiongreatest common divisornumber theory proposednumber theory