Hostname: page-component-7c8c6479df-ph5wq Total loading time: 0 Render date: 2024-03-28T20:49:24.826Z Has data issue: false hasContentIssue false

On the number of terms in the irreducible factors of a polynomial over ℚ

Published online by Cambridge University Press:  18 May 2009

A. Choudhry
Affiliation:
Deputy High Commissioner, High Commission of India, 31 Grange Road, Singapore0 923.
A. Schinzel
Affiliation:
Mathematical Institute, Polish Academy of Sciences, P.O. Box 137, 00 950 Warszawa, Poland.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

All polynomials considered in this paper belong to ℚ[x] and reducibility means reducibility over ℚ. It has been established by one of us [5] that every binomial in ℚ[x] has an irreducible factor which is either a binomial or a trinomial. He has further raised the question “Does there exist an absolute constant K such that every trinomial in ℚ[x] has a factor irreducible over ℚ which has at most K terms (i.e. K non-zero coefficients)?”

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

REFERENCES

1.Bremner, A., On reducibility of trinomials, Glasgow Math. J. 22 (1981), 155156.CrossRefGoogle Scholar
2.Dorwart, H. L., Irreducibility of polynomials, Amer. Math. Monthly 42 (1935), 369381.CrossRefGoogle Scholar
3.Dumas, G., Sur quelques cas d'irréductibilité des polynômes à coefficients rationels, Journal Math, pures appl (2) 6 (1906) 191258.Google Scholar
4.Hilbert, D., Über die Irreduzibilität ganzer rationaler Funktionen mit ganzzahligen Koeffizienten, Ges. Abh. Bd II 264286.CrossRefGoogle Scholar
5.Schinzel, A., Some unsolved problems in polynomials, Matematicka biblioteka, 25 (1963) 6370.Google Scholar
6.Schinzel, A., Selected Topics on Polynomials, (The University of Michgan Press, 1982).CrossRefGoogle Scholar
7.Verdenius, W., On the number of terms of the square and the cube of polynomials, Indag. Math. 11 (1949) 459465.Google Scholar