Geodesic
Hilbert's tenth problem
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki", Tome 1 (1973), pp. 5-37 
Yu. I. Manin. Hilbert's tenth problem. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki", Tome 1 (1973), pp. 5-37. http://geodesic.mathdoc.fr/item/INTD_1973_1_a0/
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     author = {Yu. I. Manin},
     title = {Hilbert's tenth problem},
     journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
     pages = {5--37},
     year = {1973},
     volume = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTD_1973_1_a0/}
}
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A complete account is given of a question which is of great interest to specialists in mathematical logic and number theory.