The index of small length sequences
David J. Grynkiewicz, Uzi Vishne · International Journal of Algebra and Computation · 2020
Let [Formula: see text] be a fixed integer. Define [Formula: see text] to be the unique integer in the range [Formula: see text] which is congruent to [Formula: see text] modulo [Formula: see text]. Given [Formula: see text], let [Formula: see text] and define [Formula: see text] to be the index of the sequence [Formula: see text]. If [Formula: see text] have [Formula: see text] but [Formula: see text] for all proper, non-empty subsets [Formula: see text], then a still open conjecture asserts that [Formula: see text] provided that [Formula: see text]. We give an alternative proof, that does not rely on computer calculations, verifying this conjecture when [Formula: see text] is a product of two prime powers.