A Note on Hilbert's Tenth Problem
Keyword(s):
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.
2002 ◽
Vol 43
(3)
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pp. 181-192
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2007 ◽
Vol 8
(2)
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pp. 483-491
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2013 ◽
Vol 479-480
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pp. 855-860
Keyword(s):
1995 ◽
pp. 255-258