Abstract
LetA be a primitiven-square matrix, and letq 0(A) be the smallestq such thatA q ,A q +1 have a common nonzero entry. The following general bound forq 0(A) is proved: $$q_0 (A) \leqq (n - 2)(n - 3)/2, n > 4.$$ This bound is best possible.
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