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

Source:

January 15, 2011

inductiongreatest common divisornumber theory proposednumber theory

Problem Statement

Determine all pairs

(n,m)

of positive integers for which there exists an infinite sequence

\{x_k\}

0

's and

1

's with the properties that if

x_i=0

then

x_{i+m}=1

and if

x_i = 1

then

x_{i+n} = 0.