Geodesic
Irreducibility Criteria for Polynomials with non-negative Coefficients
Canadian journal of mathematics, Tome 40 (1988) no. 2, pp. 339-351

Voir la notice de l'article provenant de la source Cambridge University Press

In [7, b.2, VIII, 128] Pólya and Szegö state the following theorem of A. Cohn:THEOREM 1. Let dndn−x ... d0 be the decimal representation of a prime. Then is irreducible.Thus, for example, since 1289 is prime, x 3 + 2x 2 +8x + 9 is irreducible. Brillhart, Odlyzko, and the author generalized Cohn's Theorem in three different directions. As examples of these types of generalizations, we note the following results, the first two of which are special cases of a result in [1] and the third of a result in [3].THEOREM 2. Let dndn−x ... d0 be the base b representation of a prime where b is an integer ≧2. Then is irreducible.THEOREM 3. Let be such that f(10) is prime and 0 ≦ dj ≦ 167 for j = 0, 1, ..., n. Then f(x) is irreducible. 
Filaseta, Michael. Irreducibility Criteria for Polynomials with non-negative Coefficients. Canadian journal of mathematics, Tome 40 (1988) no. 2, pp. 339-351. doi: 10.4153/CJM-1988-013-6
@article{10_4153_CJM_1988_013_6,
     author = {Filaseta, Michael},
     title = {Irreducibility {Criteria} for {Polynomials} with non-negative {Coefficients}},
     journal = {Canadian journal of mathematics},
     pages = {339--351},
     year = {1988},
     volume = {40},
     number = {2},
     doi = {10.4153/CJM-1988-013-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-013-6/}
}
TY  - JOUR
AU  - Filaseta, Michael
TI  - Irreducibility Criteria for Polynomials with non-negative Coefficients
JO  - Canadian journal of mathematics
PY  - 1988
SP  - 339
EP  - 351
VL  - 40
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-013-6/
DO  - 10.4153/CJM-1988-013-6
ID  - 10_4153_CJM_1988_013_6
ER  - 
%0 Journal Article
%A Filaseta, Michael
%T Irreducibility Criteria for Polynomials with non-negative Coefficients
%J Canadian journal of mathematics
%D 1988
%P 339-351
%V 40
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-013-6/
%R 10.4153/CJM-1988-013-6
%F 10_4153_CJM_1988_013_6

[1] 1. Brillhart, J., Filaseta, M. and Odlyzko, A., On an irreducibility theorem of A. Cohn, Can. J. Math. 33 (1981), 1055–1059. Google Scholar

[2] 2. Diamond, H. and Essen, M., Functions with non-negative convolutions, J. Math. Anal, and Appl. 63 (1978), 463–489. Google Scholar

[3] 3. Filaseta, M., A further generalization of an irreducibility theorem of A. Cohn, Can. J. Math. 34 (1982), 1390–1395. Google Scholar

[4] 4. McKay, J., The William Lowel Putnam mathematical competition, Amer. Math. Monthly 80 (1973), 170–178. Google Scholar

[5] 5. Meissner, E., Über positive Darstellungen von Polynomen, Math. Ann. 70 (1911), 223–235. Google Scholar

[6] 6. Ore, O., Einige Bemerkungen über Irreduzibilitat, Jahresbericht Der Deutschen Mathematiker-Vereinigung 44 (1934), 147–151. Google Scholar

[7] 7. Pólya, G. and Szegö, G., Aufgaben und Lehrsatze aus der Analysis (Springer-Verlag, Berlin, (1964). Google Scholar

Cité par Sources :