 | 1902 - 602 lapas
...theory of relative quadratic fields, f 10. DETERMINATION OF THE SOLVABILITY OF A DIOPHANTINE EQUATION. Given a diophantine equation with any number of unknown...whether the equation is solvable in rational integers. 11. QUADRATIC FORMS WITH ANY ALGEBRAIC NUMERICAL COEFFICIENTS. Our present knowledge of the theory... | |
 | Douglas M. Campbell, John C. Higgins - 1984 - 292 lapas
...procedure by which any Diophantine equation can be tested to see if solutions exist. In Hubert's words: "Given a Diophantine equation with any number of unknown...whether the equation is solvable in rational integers." Hubert does not ask for a process to find the solutions but merely for a process to determine if the... | |
 | Victor Klee, Stan Wagon - 1991 - 392 lapas
...Diophantine equations. Hubert's Tenth Problem To devise a process according to which, given a polynomial P, it can be determined by a finite number of operations whether the equation P = 0 is solvable in integers. In modern terms, this problem asks for a computer program that accepts... | |
 | I︠U︡riĭ V. Matii︠a︡sevich - 1993 - 296 lapas
...ten is about Diophantine equations: 10. DETERMINATION OF THE SOLVABILITY OF A DIOPHANTINE EQUATION Given a diophantine equation with any number of unknown...whether the equation is solvable in rational integers. Today we read the words "devise a process" to mean "find an algorithm." When Hubert's Problems were... | |
 | Julia Robinson - 1996 - 388 lapas
...century, David Hilbert proposed the following decision problem for arbitrary Diophantine equations: To devise a process according to which it can be determined by a finite namber of operations whether the equation is solvable in integers. 1 This problem was the tenth on... | |
 | Constance Reid - 1996 - 144 lapas
...short that it can be cited here in full: 10. DETERMINATION OF THE SOLVABILITY OF A DIOPHANTINE EQUATION Given a Diophantine equation with any number of unknown...whether the equation is solvable in rational integers. The tenth problem is the only one of the 23 problems that is (in today's terminology) a decision problem;... | |
 | Michael J. Sewell - 1997 - 264 lapas
...whether or not it has a solution consisting entirely of integers? In fact, Hilbert 's exact words were: 'Given a Diophantine equation with any number of unknown quantities and with integer coefficients, devise a process according to which it can be determined by a finite number of... | |
 | Solomon Feferman - 1998 - 353 lapas
...terminology, mathematically non-existent. 10. Determination of the Solvability of a Diophantine Equation Given a diophantine equation with any number of unknown...whether the equation is solvable in rational integers. Selected References In keeping with the presentation of this essay as a delivered lecture, I have given... | |
 | Keith J. Devlin - 1999 - 340 lapas
...equation has a solution. Rather, he asked for such an algorithm to be produced. To quote his own words: "Given a Diophantine equation with any number of unknown...whether the equation is solvable in rational integers." Elsewhere, however, in his lecture he says (about problems in general), "Occasionally it happens that... | |
 | Roman Murawski - 1999 - 416 lapas
...formulation was as follows (cf. English translation of (Hilbert, 1901), p. 18): Given a diophanitine equation with any number of unknown quantities and...whether the equation is solvable in rational integers. whether a given diophantine equation has solutions in integers, and the problem of solvability in natural... | |
| |
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... 
