On Hilbert's 10th Problem - Part 1 of 4

A Diophantine equation is an equation of the form $D(x_1,...,x_m)$ = 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. This lecture is part 1 of a series of 4. N.B. This video was transferred from an old encoding of the original media. The audio and video quality may be lower than normal.