Geodesic
On~he Hilbert--Kamke problem
Izvestiya. Mathematics , Tome 24 (1985) no. 1, pp. 1-47

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In this paper the author establishes the correct order (the asymptotics of the logarithm) of the number of terms in the Hilbert–Kamke problem. Bibliography: 24 titles. 
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     title = {On~he {Hilbert--Kamke} problem},
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     number = {1},
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G. I. Arkhipov. On~he Hilbert--Kamke problem. Izvestiya. Mathematics , Tome 24 (1985) no. 1, pp. 1-47. http://geodesic.mathdoc.fr/item/IM2_1985_24_1_a0/