Abstract
Let w be an infinite word and p≥2 a given positive integer. Denote by [w]p the infinite arithmetic progression modulo p of w, i.e., it is the substring of w consisting of the concatenation of the letters at positions kp for k=1,2,… We show that in the ternary case, for each p≥3 there exists an infinite square-free word w such that also the arithmetic progression [w]p is square-free. For the case p=2 there are no solutions.
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