We investigate two possible generalizations of the Cauchy–Davenport inequality |A + B| ≥ min (p, |A| + |B| − 1) for nonempty sets A, B of residues modulo a prime number p. The first one deals with another way of measuring the size of a set of points in an affine space (rather than just taking the cardinality), namely, with algebraic complexity. The second one concentrates on the multiplicative group of a field.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 432, 2015, pp. 105–110.
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Petrov, F.V., Volkov, V.V. Some Generalizations of the Cauchy–Davenport Theorem. J Math Sci 209, 874–877 (2015). https://doi.org/10.1007/s10958-015-2534-y
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DOI: https://doi.org/10.1007/s10958-015-2534-y