Estonian Winter Schools in Computer Science
Eesti arvutiteaduse talvekoolid
Steklov Institute of Mathematics (POMI)
St. Petersburg, RUSSIA
A Diophantine equation is an equation of the form
D(x1,...,xm) = 0 ,
where D is a polynomial with integer coefficients. These equations were named after the Greek mathematician Diophantus who lived in the 3rd century A.D.
Hilbert's Tenth problem can be stated as follows:
Determination of the Solvability of a Diophantine Equation. Given a diophantine equation with any number of unknown quantities and with rational integral numerical coefficients, devise a process according to which it can be determined by a finite number of operations whether the equation is solvable in rational integers.
Yu. Matiyasevich. Hilbert's Tenth Problem. V. 1. of Pacific Inst. for the Math. Sciences Distinguished Lecture Series. Pacific Inst. for the Math. Sciences, 2000. *Reproduced with permission.*
Yu. Matiyasevich. My collaboration with Julia Robinson. The Mathematical Intelligencer, v. 14, n. 4, pp. 38-45, 1992.
Sect. 10.2. from Yu. Matiyasevich. Hilbert's 10th Problem. Foundations of Computing Series. The MIT Press, 1993.
Modified Monday, Oct 12, 2015 at 17:19 EEST+0300 by firstname.lastname@example.org