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Polynomials which are near to k-th powers
Published online by Cambridge University Press: 24 October 2008
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1. Let f(x) be a polynomial of degree n ≥ 2 with integral coefficients, the highest coefficient being positive. It is well known that if f(x) is an exact k-th power for all sufficiently large integers x, where k ≥ 2, then f(x) = g(x)k identically, where g(x) is another polynomial with integral coefficients. (See Pólya and Szegö (4), section 8, problems 114, 190; also Davenport, Lewis and Schinzel(1), where other references are given.) The main purpose of this note is to prove that if we suppose only that
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- Research Article
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- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 1 , January 1965 , pp. 1 - 5
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- Copyright © Cambridge Philosophical Society 1965
References
REFERENCES
(1)Davenport, H., Lewis, D. J. and Schinzel, A.Polynomials of certain special types. Acta Arith. 9 (1964), 107–116.CrossRefGoogle Scholar
(2)Dörge, K.Zum Hilbertschen Irreduzibilitätssatz. Math. Ann. 95 (1926), 84–97.CrossRefGoogle Scholar
(3)Dörge, K.Einfacher Beweis des Hilbertschen Irreduzibilitätssatzes. Math. Ann. 96 (1927), 176–182.CrossRefGoogle Scholar
(4)Pólya, G. and Szegö, G.Aufgaben und Lehrsätze aus der Analysis, vol. ii (Berlin, 1925).Google Scholar
(6)Weyl, H.Ueber die Gleichverteilung von Zahlen mod. Eins. Math. Ann. 77 (1916), 313–352.CrossRefGoogle Scholar