Hilbert's Tenth Problem

Statement of the problem
(in English)

10. Determination of the solvability of a Diophantine equation. Given a diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined by a finite number of operations whether the equation is solvable in rational integers.

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Laboratory of Mathematical Logic at
St. Petersburg Division of Steklov Institute of Mathematics (POMI) of
Russian Academy of Sciences