We prove a mean-value theorem for polynomials of a special form. We investigate the case of a sum over the vertices of a regular polygon and obtain a criterion for an equation of a special form to be satisfied.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 5, pp. 699–707, May, 2011.
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Trofymenko, O.D. Analog of the mean-value theorem for polynomials of special form. Ukr Math J 63, 815–826 (2011). https://doi.org/10.1007/s11253-011-0544-6
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DOI: https://doi.org/10.1007/s11253-011-0544-6