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quasigroup; functional equation; distributive quasigroup; distributive-like functional equation; quasigroup solution; solution set; quasigroup identity; parastrophic equivalence

References:

[1] Aczél J.: **Lectures on Functional Equations and Their Applications**. Academic Press, New York, London, 1966. MR 0208210

[2] Aczél J., Belousov V.D., Hosszú M.: **Generalized associativity and bisymmetry on quasigroups**. Acta. Math. Acad. Sci. Hungar. 11 (1960), no. 12-2, 127-136. DOI 10.1007/BF02020630 | MR 0140600

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[4] Belousov V.D.: **Cross isotopy of quasigroup**. Quasigroups and Their Systems, Shtiintsa, Kishinev (1990), 14–20 (in Russian).

[5] Belousov V.D.: **Some remarks on the functional equation of generalized distributivity**. Aequationes Math. 1 (1968), no. 1–2, 54–65. DOI 10.1007/BF01817557 | MR 0228610 | Zbl 0157.46402

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[8] Krainichuk H.V., Sokhatsky F.M.: **Solving of some functional equations having invertible binary functions**. Academ. Ya.S. Pidstryhach Conf. of Young Scientists “Modern problems of Math. and Mech”, Lviv Ivan Franko National University, Lviv, 2009, pp. 158–159 (in Ukrainian).

[9] Krapež A., Živković D.: **Parastrophically equivalent quasigroup equations**. Publ. Inst. Math. (Beograd) (N.S.), 87(101), (2010), 39–58. DOI 10.2298/PIM1001039K | MR 2642000

[10] Krapež A., Simić S.K., Tošić D.V.: **Parastrophically uncancellable quasigroup equations**. Aequationes Math. 79 (2010), 261-280. DOI 10.1007/s00010-010-0016-3 | MR 2665535 | Zbl 1217.39032

[11] Sokhatsky F.M.: **On classification of functional equations on quasigroups**. Ukrainian Math. J. 56 (2004), no. 4, 1259–1266 (in Ukrainian). MR 2133028

[12] Sokhatsky F.M.: **On classification of distributive-like functional equations**. Book of Abstracts of the $8^{th}$ International Algebraic Conference in Ukraine, July 5–12 (2011), Lugansk, Ukraine, p. 79.