Universal Hilbert subsets
1998 ◽
Vol 124
(1)
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pp. 127-134
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We show that the sequence 2n+n is a universal Hilbert sequence. That is, for each polynomial P(T, Y) irreducible in ℚ(T) [Y], the polynomial P(2n+n, Y) is irreducible in ℚ[Y] for all but finitely many n. This answers a question of M. Yasumoto. Other examples, like 2n+5n, are given. They are all obtained as special cases of a more general result which is proved from classical diophantine arguments.
2019 ◽
Vol 7
(1)
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pp. 250-252
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1975 ◽
Vol 78
(2)
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pp. 301-307
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2007 ◽
Vol 44
(01)
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pp. 199-211
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Keyword(s):
2016 ◽
Vol 59
(2)
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pp. 323-348
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Keyword(s):
1987 ◽
Vol 411
(1841)
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pp. 285-303
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Keyword(s):
1995 ◽
Vol 450
(1939)
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pp. 391-416
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Keyword(s):
2007 ◽
Vol 44
(1)
◽
pp. 199-211
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Keyword(s):
Keyword(s):