= Solution
\b[True.] A length-$d$ <linear-feedback shift register> has $2^d-1$ nonzero fills, and its first $d$ output bits recover its fill, so these fills give distinct output <sequences>. If lengths satisfy $r<s$, the longer register has strictly more nonzero outputs. At least one is absent from the shorter register's output set; choosing any nonzero shorter fill then gives unequal outputs. This is the counting property of <output sets of different-length linear-feedback registers>.
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