Diophantine Set - Application To Hilbert's Tenth Problem

Application To Hilbert's Tenth Problem

Hilbert's tenth problem asks for a general algorithm deciding the solvability of Diophantine equations. The conjunction of Matiyasevich's theorem with earlier results known collectively as the MRDP theorem implies that a solution to Hilbert's tenth problem is impossible.

Read more about this topic:  Diophantine Set

Famous quotes containing the words application to, application, tenth and/or problem:

    The receipt to make a speaker, and an applauded one too, is short and easy.—Take of common sense quantum sufficit, add a little application to the rules and orders of the House, throw obvious thoughts in a new light, and make up the whole with a large quantity of purity, correctness, and elegancy of style.
    Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)

    We will not be imposed upon by this vast application of forces. We believe that most things will have to be accomplished still by the application called Industry. We are rather pleased, after all, to consider the small private, but both constant and accumulated, force which stands behind every spade in the field. This it is that makes the valleys shine, and the deserts really bloom.
    Henry David Thoreau (1817–1862)

    They say all lovers swear more performance than they are able, and yet reserve an ability that they never perform; vowing more than the perfection of ten, and discharging less than the tenth part of one.
    William Shakespeare (1564–1616)

    The problem for the King is just how strict
    The lack of liberty, the squeeze of the law
    And discipline should be in school and state....
    Robert Frost (1874–1963)