Geodesic
Multidimensional system of Diophantine equations
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2017), pp. 68-71
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An asymptotics for number of solutions of system of three Diophantine equations of the additive type in six variables was found. The each additive summand of these equations represents the simplest form of which degree in each variable does not exceed 1. 
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R. V. Pocherevin. Multidimensional system of Diophantine equations. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2017), pp. 68-71. http://geodesic.mathdoc.fr/item/VMUMM_2017_1_a12/

[1] Hua L.K., “On the number of solutions of Tarry's problem”, Acta Scientia Sinica, 1952, no. 1, 1–76 | MR

[2] Arkhipov G.I., Karatsuba A.A., Chubarikov V.N., Teoriya kratnykh trigonometricheskikh summ, Nauka, M., 1987 | MR