A Note on Hilbert's Tenth Problem
Canadian mathematical bulletin, Tome 3 (1960) no. 2, pp. 153-156
Voir la notice de l'article provenant de la source Cambridge University Press
The tenth problem on Hilbert's well known list [1] is the following.(H 10) For an arbitrary polynomial P = P(x1,x2,...,xn) with integer coefficients to determine whether or not the equation P = 0 has a solution in integers.By 'integers' we always mean 'rational integers'. The problem (H 10) is still unsolved but it appears likely that no decision procedure exists; in this connection see [2]. It will be shown here that (H 10) is equivalent to deciding whether or not every member of a certain given countable sec of rational functions of a single variable x is absolutely monotonie. We recall that f(x) is absolutely monotonie in I if f(x) possesses non-negative derivatives of all orders at every x ∊ I.
Melzak, Z. A. A Note on Hilbert's Tenth Problem. Canadian mathematical bulletin, Tome 3 (1960) no. 2, pp. 153-156. doi: 10.4153/CMB-1960-019-9
@article{10_4153_CMB_1960_019_9,
author = {Melzak, Z. A.},
title = {A {Note} on {Hilbert's} {Tenth} {Problem}},
journal = {Canadian mathematical bulletin},
pages = {153--156},
year = {1960},
volume = {3},
number = {2},
doi = {10.4153/CMB-1960-019-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1960-019-9/}
}
[1] 1. Hilbert, D., Mathematical problems, Bull. Amer. Math, Soc. 8 (1901), 437-479. Google Scholar
[2] 2. Davis, M., Computability and Unsolvability, (New York, 1958). Google Scholar
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