Uniform bounds for the number of solutions to Yn = f(X)
1986 ◽
Vol 100
(2)
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pp. 237-248
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Keyword(s):
The Past
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Let K be an algebraic number field and f(X) ∈ K[X]. The Diophantine problem of describing the solutions to equations of the formhas attracted considerable interest over the past 60 years. Siegel [12], [13] was the first to show that under suitable non-degeneracy conditions, the equation (+) has only finitely many integral solutions in K. LeVeque[7] proved the following, more explicit, result. Letwhere a ∈ K* and αl,…,αk are distinct and algebraic over K. Then (+) has only finitely many integral solutions unless (nl,…,nk) is a permutation of one of the n-tuples
Keyword(s):
1977 ◽
Vol 18
(1)
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pp. 109-111
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1999 ◽
Vol 42
(1)
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pp. 127-141
Keyword(s):
1981 ◽
Vol 89
(1)
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pp. 1-5
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Keyword(s):
1967 ◽
Vol 63
(3)
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pp. 693-702
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1993 ◽
Vol 113
(3)
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pp. 449-460
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Keyword(s):
1963 ◽
Vol 3
(4)
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pp. 408-434
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1976 ◽
Vol 15
(1)
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pp. 33-57
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1966 ◽
Vol 6
(4)
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pp. 399-401