We present two sets of 12 integers that have the same sets of 4-sums. The proof of the fact that a set of 12 numbers is uniquely determined by the set of its 4-sums published 50 years ago is wrong, and we demonstrate an incorrect calculation in it.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 448, 2016, pp. 135–142.
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Isomurodov, J.E., Kokhas, K.P. A Set of 12 Numbers is Not Determined by the Set of its 4-Sums. J Math Sci 224, 258–262 (2017). https://doi.org/10.1007/s10958-017-3411-7
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DOI: https://doi.org/10.1007/s10958-017-3411-7